Finite Group DatabasebetaFinite Group Databasebeta| order | 23210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×#26042441 |
| Fitting, socle, Hall | C2×C11×C211 ⋊ C5 |
| derived, Hall | C11×C211 ⋊ C2×C5 |
| Hall | C2×C211 ⋊ C11⋊C5 |
| Sylow | C211 ⋊ C2×C11⋊C5 |
| Hall | C2×C11 ⋊ C211⋊C5 |
| Sylow | C11 ⋊ C2×C211⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #26042441 |
| commutator, cosocle, hypocenter | C11×C211 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C211 | C5 |
| LCS | G ▷ C11×C211 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4642 |
938 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23210, 5);