Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C11 |
| unambiguous semidirect product | D19⋊((C11⋊D11)⋊C3) |
| unambiguous semidirect product | #28352261⋊C2 |
| unambiguous semidirect product | ((C11⋊D11)⋊(C19⋊C3))⋊C2 |
| unambiguous semidirect product | (D19⋊(C112⋊C3))⋊C2 |
| Fitting, socle, derived, Hall | C112×C19 ⋊ C22×C3 |
| Hall | D19×C11⋊D11 ⋊ C3 |
| Hall | C19⋊(C112⋊C3) ⋊ C22 |
| Sylow | C112 ⋊ C2×D19⋊C3 |
| Sylow | C19 ⋊ C2×(C11⋊D11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C19 | C22×C3 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 627 |
Polycyclic presentation:
2^2,3,11^2,19|f^a=f^18,d^b=d^10,e^b=e^10,d^c=d^3e^9,e^c=de^7,f^c=f^7238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 67);