Finite Group DatabasebetaFinite Group Databasebeta| order | 25050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(C5⋊D835) |
| unambiguous semidirect product | C5⋊D2505 |
| unambiguous semidirect product | C167⋊(C3⋊(C5⋊D5)) |
| Fitting, socle, derived, Hall | C3×C52×C167 ⋊ C2 |
| Hall | C52×C167 ⋊ D3 |
| Hall | C3×C167 ⋊ C5⋊D5 |
| Sylow | C167 ⋊ C3⋊(C5⋊D5) |
| Hall | C3×C52 ⋊ D167 |
| Sylow | C52 ⋊ D501 |
| Sylow | C3 ⋊ C5⋊D835 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C167 | C2 |
| LCS | G ▷ C3×C52×C167 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12525 |
Polycyclic presentation:
2,3,5^2,167|b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^1666264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25050, 26);