Finite Group DatabasebetaFinite Group Databasebeta| order | 27225 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C11 |
| direct product | C25×C112⋊C9 |
| unambiguous semidirect product | (C112×C25)⋊C9 |
| derived, Sylow | C112 ⋊ C9×C25 |
| Hall | C112×C25 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C25 | C112⋊C3 |
| commutator, hypocenter | C112 | C9×C25 |
| Frattini | C3×C5 | C5×C112⋊C3 |
| Fitting | C3×C112×C25 | C3 |
| socle, prime radical, cosocle | C3×C5×C112 | C3×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C3×C25 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2475 |
3225 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27225, 14);