Finite Group DatabasebetaFinite Group Databasebeta| order | 10832 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#14582142 |
| Fitting | C4×C677 ⋊ C4 |
| derived, Sylow | C677 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14582142 |
| commutator, hypocenter | C677 | C42 |
| Frattini | C2 | C2×#14582142 |
| Fitting | C4×C677 | C4 |
| socle | C2×C677 | C2×C4 |
| prime radical, cosocle | C2×D677 | C22 |
| LCS | G ▷ C677 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
692 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14582142, #36343500, #36343510, … |
| maximal normal subgroup of | C8×#14582142, #36343500, #36343510, … |
| maximal quotient of | (C2×#14582142)⋊C4, C8×#14582142, C4×#19129319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10832, 44);