Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10624391⋊D19 |
| Fitting, socle, Hall | C112×C19 ⋊ C2×D3 |
| derived, Hall | C19×C112⋊C3 ⋊ C22 |
| Hall | C112⋊C3 ⋊ C2×D19 |
| Sylow | C112 ⋊ D3×D19 |
| Sylow | C19 ⋊ #10624391⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C19×C112⋊C3 | C22 |
| Fitting, socle | C112×C19 | C2×D3 |
| LCS | G ▷ C19×C112⋊C3 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 627 |
Polycyclic presentation:
2^2,3,19,11^2|c^a=c^2,d^a=d^18,e^a=ef,f^a=f^10,c^b=c^2,e^b=e^10f^10,e^c=f,f^c=e^10f^10373 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 76);