Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×#261 |
| Fitting | C2×C8×C13 ⋊ C4 |
| derived, Sylow | C13 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #261 |
| commutator, hypocenter | C13 | C2×C4×C8 |
| Frattini | C4 | C22×#261 |
| Fitting | C2×C8×C13 | C4 |
| socle | C22×C13 | C42 |
| prime radical | C22×D13 | C2×C4 |
| cosocle | C4×D13 | C23 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C8 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#261)⋊C16, #13129879, C4×C8×#261, … |
| maximal normal subgroup of | (C2×#261)⋊C16, #13129879, C4×C8×#261, … |
| maximal quotient of | C2×C8×#1057, C8×D13⋊C8, C2×#1057⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1053);