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×#473 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #121 |
| commutator, Frattini, cosocle | C2×C4 | C23×C13 |
| prime radical | C13×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ G | |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,25)(16,26,30,36)(17,31,33,39)(18,24,19,23)(21,29,37,28)(22,34,38,32)(27,41,43,35)(40,44,45,42);(14,16,19,29,20,30,18,28)(15,21,24,36,25,37,23,26)(17,27,34,44,33,43,32,42)(22,35,39,45,38,41,31,40);(14,17)(15,22)(16,27)(18,32)(19,34)(20,33)(21,35)(23,31)(24,39)(25,38)(26,40)(28,42)(29,44)(30,43)(36,45)(37,41)208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 974);