Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #360 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#362 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #102 |
| commutator | C8 | C2×C4×C13 |
| Frattini, cosocle | C2×C8 | C22×C13 |
| prime radical | C22×C13 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C8×C13 ◁ G | |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 2 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,22,19,24,34,23)(16,25,27,38,28,42,33,41)(17,29,31,21,32,39,45,40)(20,30,35,26,37,43,36,44);(14,16,19,28)(15,20,24,37)(17,30,32,43)(18,33,34,27)(21,38,40,41)(22,36,23,35)(25,29,42,39)(26,31,44,45)208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 167);