Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C22 |
| direct product | C8×Q8×C13 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C22 |
| commutator | C2 | C22×C8×C13 |
| Frattini, cosocle | C2×C4 | C23×C13 |
| socle, prime radical | C22×C13 | C22×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ G | |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8)(17,18,19,20,21,22,23,24,25,26,27,28,29);(9,10,11,12)(13,16,15,14);(9,13,11,15)(10,14,12,16)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 946);