Finite Group DatabasebetaFinite Group Databasebeta| order | 23550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C5⋊D5×C157⋊C3 |
| unambiguous semidirect product | C5⋊(D5×C157⋊C3) |
| Fitting, socle, derived, Hall | C52×C157 ⋊ C2×C3 |
| Hall | C52×C157⋊C3 ⋊ C2 |
| Hall | C5⋊D5×C157 ⋊ C3 |
| Sylow | C157 ⋊ C3×C5⋊D5 |
| Sylow | C52 ⋊ C2×C157⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C157 | C2×C3 |
| LCS | G ▷ C52×C157 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3925 |
770 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23550, 26);