Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#123 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C31 |
| prime radical | C2×D4×C31 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ G | |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 496 |
A minimal faithful permutation representation — 3 generators on 43 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)(33,35)(37,40)(38,42);(36,37)(38,41)(39,40)(42,43);(32,33)(34,35)(36,38,39,42)(37,41,40,43)434 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 158);