Finite Group DatabasebetaFinite Group Databasebeta| order | 25050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C167⋊#3874 |
| Fitting, socle, Hall | C52×C167 ⋊ D3 |
| derived, Hall | C52⋊C3×C167 ⋊ C2 |
| Sylow | C167 ⋊ #3874 |
| Hall | C52⋊C3 ⋊ D167 |
| Sylow | C52 ⋊ D501 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52⋊C3×C167 | C2 |
| Fitting, socle | C52×C167 | D3 |
| LCS | G ▷ C52⋊C3×C167 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2505 |
Polycyclic presentation:
2,3,167,5^2|b^a=b^2,c^a=c^166,d^a=de^2,e^a=e^4,d^b=d^3e^3,e^b=d^4e926 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25050, 12);