Finite Group DatabasebetaFinite Group Databasebeta| order | 27612 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13×C59 · Schur multiplier (H2) = C3 |
| direct product | C13×#157×C59 |
| Fitting, socle, Hall | C32×C13×C59 ⋊ C4 |
| derived, Sylow | C32 ⋊ C4×C13×C59 |
| Hall | C32×C59 ⋊ C4×C13 |
| Hall | C32×C13 ⋊ C4×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C59 | #157 |
| commutator, hypocenter | C32 | C4×C13×C59 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C59 | C4 |
| prime radical | C13×C3⋊D3×C59 | C2 |
| cosocle | C3⋊D3 | C2×C13×C59 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C13×C59 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4602 |
4602 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27612, 81);