Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C19⋊#13089721 |
| Fitting, socle, Hall | C112×C19 ⋊ Dic3 |
| derived, Hall | C19×C112⋊C3 ⋊ C4 |
| Hall | C112⋊C3 ⋊ Dic19 |
| Sylow | C112 ⋊ Dic57 |
| Sylow | C19 ⋊ #13089721 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C19×C112⋊C3 | C4 |
| Fitting, socle | C112×C19 | Dic3 |
| prime radical, cosocle | C19×(C11⋊D11)⋊C3 | C2 |
| LCS | G ▷ C19×C112⋊C3 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1254 |
Polycyclic presentation:
2^2,3,19,11^2|a^2=b,c^a=c^2,d^a=d^18,e^a=e^10f^7,f^a=e^6f,e^b=e^10,f^b=f^10,e^c=e^5f^7,f^c=e^5f^5250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 70);