Finite Group DatabasebetaFinite Group Databasebeta| order | 23002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D217 |
| unambiguous semidirect product | C7⋊(C53×D31) |
| unambiguous semidirect product | C31⋊(D7×C53) |
| Fitting, socle, Hall | C7×C31×C53 ⋊ C2 |
| derived, Hall | C7×C31 ⋊ C2×C53 |
| Hall | C31×C53 ⋊ D7 |
| Hall | C7×C53 ⋊ D31 |
| Sylow | C31 ⋊ D7×C53 |
| Sylow | C7 ⋊ C53×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D217 |
| commutator, cosocle, hypocenter | C7×C31 | C2×C53 |
| Frattini | C1 | G |
| Fitting, socle | C7×C31×C53 | C2 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C53 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11501 |
5830 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23002, 7);