Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×D11×D23 |
| Fitting, socle, Hall | C52×C11×C23 ⋊ C22 |
| derived, Hall | C11×C23 ⋊ C22×C52 |
| Hall | C52×C23 ⋊ C2×D11 |
| Hall | C52×C11 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C52×D11 |
| Sylow | C11 ⋊ C2×C52×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D11×D23 |
| commutator, cosocle, hypocenter | C11×C23 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C11×C23 | C22 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 ◁ C52 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6325 |
2275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 113);