Finite Group DatabasebetaFinite Group Databasebeta| order | 27225 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C52 · Schur multiplier (H2) = C3×C5 |
| direct product | C32×C5×#10597243 |
| Fitting, socle | C32×C5×C112 ⋊ C5 |
| derived, Sylow | C112 ⋊ C32×C52 |
| Hall | C32×C112 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | #10597243 |
| commutator, cosocle, hypocenter | C112 | C32×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C112 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C32×C5 | |
672 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5445 |
1305 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27225, 40);