Finite Group DatabasebetaFinite Group Databasebeta| order | 24225 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C5 |
| Fitting, socle, Hall | C52×C17×C19 ⋊ C3 |
| derived, Hall | C52×C19 ⋊ C3×C17 |
| Hall | C52×C17 ⋊ C19⋊C3 |
| Hall | C17×C19 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ C17×C19⋊C3 |
| Sylow | C19 ⋊ C17×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C19⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×C19 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C19 | C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C17 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4845 |
2737 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24225, 5);