Finite Group DatabasebetaFinite Group Databasebeta| order | 27468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C109 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D9×C109 |
| unambiguous semidirect product | C9⋊(C22×C7×C109) |
| unambiguous semidirect product | (C2×C9)⋊(C2×C7×C109) |
| Fitting | C2×C7×C9×C109 ⋊ C2 |
| derived, Sylow | C9 ⋊ C22×C7×C109 |
| Hall | C7×C9×C109 ⋊ C22 |
| Hall | C9×C109 ⋊ C22×C7 |
| Hall | C7×C9 ⋊ C22×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C109 | D9 |
| commutator, cosocle, hypocenter | C9 | C22×C7×C109 |
| Frattini | C3 | C2×D3×C7×C109 |
| Fitting | C2×C7×C9×C109 | C2 |
| socle | C2×C3×C7×C109 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C7×C109 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13734 |
9156 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27468, 73);