Finite Group DatabasebetaFinite Group Databasebeta| order | 27564 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#22604030 |
| Fitting, socle, derived, Hall | C3×C2297 ⋊ C4 |
| Sylow | C2297 ⋊ Dic3 |
| Sylow | C3 ⋊ #22604030 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C2297 | C4 |
| prime radical, cosocle | C3×D2297 | C2 |
| LCS | G ▷ C3×C2297 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6891 |
Polycyclic presentation:
2^2,3,2297|a^2=b,c^a=c^2,d^a=d^1932,d^b=d^22961728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27564, 7);