Finite Group DatabasebetaFinite Group Databasebeta| order | 56882 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C2×C17×C239⋊C7 |
| Fitting, socle, Hall | C2×C17×C239 ⋊ C7 |
| derived, Sylow | C239 ⋊ C2×C7×C17 |
| Hall | C17×C239 ⋊ C2×C7 |
| Hall | C2×C239 ⋊ C7×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | C239⋊C7 |
| commutator, cosocle, hypocenter | C239 | C2×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C239 | C7 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C2×C17 | |
16 conjugacy classes of subgroups.
1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(56882, 3);