Finite Group DatabasebetaFinite Group Databasebeta| order | 27612 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C59⋊#90866 |
| Fitting, socle, derived, Hall | C32×C13×C59 ⋊ C4 |
| Hall | C13×C59 ⋊ #157 |
| Hall | C32×C59 ⋊ #261 |
| Hall | C32×C13 ⋊ Dic59 |
| Sylow | C59 ⋊ #90866 |
| Sylow | C13 ⋊ C59⋊#157 |
| Sylow | C32 ⋊ C59⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C13×C59 | C4 |
| prime radical, cosocle | C59×C3⋊D39 | C2 |
| LCS | G ▷ C32×C13×C59 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4602 |
Polycyclic presentation:
2^2,3^2,13,59|a^2=b,c^a=cd,d^a=cd^2,e^a=e^5,f^a=f^58,c^b=c^2,d^b=d^2,e^b=e^121773 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27612, 84);