Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C29 · Schur multiplier (H2) = C2 |
| direct product | C29×#126 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C29 |
| prime radical | C23×C29 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ G | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 464 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(31,35)(32,39)(37,44)(38,42)(40,43)(41,45);(30,31,36,42)(32,37,43,44)(33,35,34,38)(39,45,40,41);(30,32,33,40)(31,37,35,41)(34,39,36,43)(38,45,42,44)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 187);