Finite Group DatabasebetaFinite Group Databasebeta| order | 24700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×D13×D19 |
| unambiguous semidirect product | (C19×D13)⋊(C2×C52) |
| unambiguous semidirect product | (C13×D19)⋊(C2×C52) |
| unambiguous semidirect product | D247⋊(C2×C52) |
| Fitting, socle, Hall | C52×C13×C19 ⋊ C22 |
| derived, Hall | C13×C19 ⋊ C22×C52 |
| Hall | C52×C19 ⋊ C2×D13 |
| Hall | C52×C13 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×C52×D13 |
| Sylow | C13 ⋊ C2×C52×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D13×D19 |
| commutator, cosocle, hypocenter | C13×C19 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C19 | C22 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C52 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6175 |
2200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24700, 51);