Finite Group DatabasebetaFinite Group Databasebeta| order | 24850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5 |
| direct product | C52×D71⋊C7 |
| unambiguous semidirect product | (C52×D71)⋊C7 |
| Fitting, socle, Hall | C52×C71 ⋊ C2×C7 |
| derived, Sylow | C71 ⋊ C2×C52×C7 |
| Hall | C52×C71⋊C7 ⋊ C2 |
| Hall | C52×D71 ⋊ C7 |
| Hall | C71⋊C7 ⋊ C2×C52 |
| Hall | D71 ⋊ C52×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D71⋊C7 |
| commutator, cosocle, hypocenter | C71 | C2×C52×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C71 | C2×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1775 |
475 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24850, 24);