Finite Group DatabasebetaFinite Group Databasebeta| order | 56882 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C2×(C239⋊C7)⋊C17 |
| Fitting, socle, Hall | C2×C239 ⋊ C7×C17 |
| derived, Sylow | C239 ⋊ C2×C7×C17 |
| Hall | C2×C239⋊C17 ⋊ C7 |
| Hall | C239⋊C17 ⋊ C2×C7 |
| Hall | C2×C239⋊C7 ⋊ C17 |
| Hall | C239⋊C7 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C239⋊C7)⋊C17 |
| commutator, cosocle, hypocenter | C239 | C2×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C239 | C7×C17 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(56882, 4);