Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C29 · Schur multiplier (H2) = C22 |
| direct product | C29×#135 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | D4 |
| commutator, Frattini, cosocle | C4 | C23×C29 |
| socle | C2×C29 | C2×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C2×C4×C29 ◁ G | |
62 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)(30,31)(32,39)(33,37)(34,42)(35,38)(36,40)(41,44)(43,45);(30,32)(31,36)(33,40)(34,43)(35,41)(37,44)(38,45)(39,42);(30,33,35,34)(31,37,38,42)(32,40,41,43)(36,44,45,39)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 196);