Finite Group DatabasebetaFinite Group Databasebeta| order | 27612 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C59 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×C3×C13⋊C3×C59 |
| Fitting, socle | C22×C3×C13×C59 ⋊ C3 |
| derived, Sylow | C13 ⋊ C22×C32×C59 |
| Hall | C22×C13×C59 ⋊ C32 |
| Hall | C13×C59 ⋊ C22×C32 |
| Hall | C22×C13 ⋊ C32×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C59 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C22×C32×C59 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C13×C59 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C3×C59 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9204 |
4956 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27612, 118);