About this representation
Group
 Th

Group generators
 Standard generators

Dimension
 248

Ring
 GF(3)

Characteristic
 3

Irreducibility information
 Absolutely irreducible

Indicator
 +

Character
 φ_{2}

Character ring
 Z

Schur index
 1

Dimension of 1cohomology
 0

Notes
 Invariant quadratic form is of plus type.
A nonsplit extension 3^{248}.Th is known to exist.

Contributed by
 Not recorded

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Checks applied
Check 
Description 
Date 
Checked by 
Result 
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
