Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#509 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×D8 |
| commutator, Frattini, cosocle | C8 | C23×C13 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C8×C13 ◁ G | |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,26)(18,20)(21,23)(22,24)(25,27)(28,29);(15,19)(16,23)(17,24)(20,27)(21,22)(25,29)(26,28);(15,20)(19,27)(21,28)(22,26)208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1010);