Finite Group DatabasebetaFinite Group Databasebeta| order | 23450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C67 · Schur multiplier (H2) = C1 |
| direct product | C7×D25×C67 |
| unambiguous semidirect product | C25⋊(C2×C7×C67) |
| Fitting, Hall | C7×C25×C67 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C7×C67 |
| Hall | C25×C67 ⋊ C2×C7 |
| Hall | C7×C25 ⋊ C2×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C67 | D25 |
| commutator, cosocle, hypocenter | C25 | C2×C7×C67 |
| Frattini | C5 | C7×D5×C67 |
| Fitting | C7×C25×C67 | C2 |
| socle | C5×C7×C67 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C7×C67 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11725 |
6566 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23450, 5);