Finite Group DatabasebetaFinite Group Databasebeta| order | 25550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D511 |
| unambiguous semidirect product | C7⋊(C52×D73) |
| unambiguous semidirect product | C73⋊(C52×D7) |
| Fitting, socle, Hall | C52×C7×C73 ⋊ C2 |
| derived, Hall | C7×C73 ⋊ C2×C52 |
| Hall | C52×C73 ⋊ D7 |
| Hall | C52×C7 ⋊ D73 |
| Sylow | C73 ⋊ C52×D7 |
| Sylow | C7 ⋊ C52×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D511 |
| commutator, cosocle, hypocenter | C7×C73 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C73 | C2 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12775 |
6425 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25550, 12);