About this representation
Group
 A_{5}

Group generators
 Standard generators

Dimension
 4

Distinguishing letter
 a

Ring
 GF(2)

Characteristic
 2

Description
 Natural representation as O_{4}^{−}(2)

Irreducibility information
 Absolutely irreducible

Indicator
 +

Character
 φ_{4}

Character ring
 Z

Schur index
 1

Dimension of 1cohomology
 0

Dimension of 2cohomology
 0

Contributed by
 Not recorded

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This representation is available in the following formats:
Checks applied
Check 
Description 
Date 
Checked by 
Result 
Presentation
 Check against the relations in a presentation. If this test passes, then the group is of the correct isomorphism type, and the generators are those stated. Note that the presentation itself is not checked here.
 Jul 4, 2006
 certify.pl version 0.05
 Pass

Semipresentation
 Check against a semipresentation. If this fails, then the representation is not on standard generators, and may generate the wrong group. Note that the semipresentation itself is not checked here.
 Jul 4, 2006
 certify.pl version 0.05
 Pass

Dimension/field
 Check the dimension and field/ring of the representation.
 Jul 4, 2006
 certify.pl version 0.05
 Pass

Files exist
 Check whether files exist (where stated).
 Jul 4, 2006
 certify.pl version 0.05
 Pass

Irreducibility
 Check the irreducibility type is correct.
 Jul 5, 2006
 irr.pl v0.2
 Pass
