Finite Group DatabasebetaFinite Group Databasebeta| order | 24450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D163⋊C3 |
| unambiguous semidirect product | D163⋊(C3×C52) |
| unambiguous semidirect product | (C163⋊C3)⋊(C2×C52) |
| unambiguous semidirect product | (C5×D163)⋊(C3×C5) |
| Fitting, socle, Hall | C52×C163 ⋊ C2×C3 |
| derived, Sylow | C163 ⋊ C2×C3×C52 |
| Hall | C52×C163⋊C3 ⋊ C2 |
| Hall | C52×D163 ⋊ C3 |
| Hall | C163⋊C3 ⋊ C2×C52 |
| Hall | D163 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D163⋊C3 |
| commutator, cosocle, hypocenter | C163 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C163 | C2×C3 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4075 |
825 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24450, 22);