Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#6131 |
| Fitting | C22×Q8×C13 ⋊ C2 |
| Sylow | C13 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D13 |
| commutator, cosocle | C2×C13 | C25 |
| Frattini | C2 | C24×D13 |
| Fitting | C22×Q8×C13 | C2 |
| socle | C23×C13 | C23 |
| hypercenter | C22×Q8 | D13 |
| hypocenter | C13 | C22×#41 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
890 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #13114763, #13114775, #13117325, … |
| maximal normal subgroup of | #13114763, #13114775, #13117325, … |
| maximal quotient of | C22×#88146, C22×#88147, C22×Q8×Dic13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1609);