Finite Group DatabasebetaFinite Group Databasebeta| order | 25050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C167 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D5×C167 |
| unambiguous semidirect product | C5⋊(C2×C3×C5×C167) |
| Fitting, socle, Hall | C3×C52×C167 ⋊ C2 |
| derived | C5 ⋊ C2×C3×C5×C167 |
| Hall | C52×C167 ⋊ C2×C3 |
| Hall | C3×C52 ⋊ C2×C167 |
| Sylow | C52 ⋊ C2×C3×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C167 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C3×C5×C167 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C167 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C3×C5×C167 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5010 |
10020 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25050, 17);