Finite Group DatabasebetaFinite Group Databasebeta| order | 24450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | D163⋊(C52⋊C3) |
| Fitting, socle, derived, Hall | C52×C163 ⋊ C2×C3 |
| Hall | C52⋊(C163⋊C3) ⋊ C2 |
| Hall | C52×D163 ⋊ C3 |
| Hall | D163 ⋊ C52⋊C3 |
| Sylow | C163 ⋊ C2×C52⋊C3 |
| Sylow | C52 ⋊ D163⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C163 | C2×C3 |
| LCS | G ▷ C52×C163 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2445 |
Polycyclic presentation:
2,3,5^2,163|e^a=e^162,c^b=c^3d^2,d^b=cd,e^b=e^104697 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24450, 16);