Finite Group DatabasebetaFinite Group Databasebeta| order | 24525 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C52⋊C3×C109⋊C3 |
| unambiguous semidirect product | (C52⋊(C109⋊C3))⋊C3 |
| unambiguous semidirect product | (C52⋊C3×C109)⋊C3 |
| unambiguous semidirect product | (C52×C109⋊C3)⋊C3 |
| Fitting, socle, derived, Hall | C52×C109 ⋊ C32 |
| Sylow | C109 ⋊ C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×C109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C109 | C32 |
| LCS | G ▷ C52×C109 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1635 |
429 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24525, 12);