Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#555 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,21)(18,19)(23,24)(27,28);(15,19)(17,20)(22,23,26,24)(25,28,29,27);(14,16,18,21)(15,20,19,17)(22,24,26,23)(25,28,29,27);(14,17,18,20)(15,21,19,16)(22,25,26,29)(23,27,24,28)325 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1556);