Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#472 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #121 |
| commutator, Frattini, cosocle | C2×C4 | C23×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ G | |
108 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)(15,19)(16,23)(17,20)(22,27)(24,25)(26,28);(14,15,20,27,18,22,17,19)(16,21,23,28,25,29,24,26);(14,16)(15,21)(17,24)(18,25)(19,26)(20,23)(22,29)(27,28)208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 973);