Finite Group DatabasebetaFinite Group Databasebeta| order | 23030 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C7 |
| direct product | C47×C5⋊(C7⋊D7) |
| unambiguous semidirect product | C5⋊(C47×C7⋊D7) |
| unambiguous semidirect product | C7⋊(C47×D35) |
| Fitting, socle, Hall | C5×C72×C47 ⋊ C2 |
| derived, Hall | C5×C72 ⋊ C2×C47 |
| Hall | C72×C47 ⋊ D5 |
| Hall | C5×C47 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D5×C47 |
| Sylow | C5 ⋊ C47×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | C5⋊(C7⋊D7) |
| commutator, cosocle, hypocenter | C5×C72 | C2×C47 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C47 | C2 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C47 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11515 |
5828 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23030, 19);