Finite Group DatabasebetaFinite Group Databasebeta| order | 27588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C11 |
| direct product | C2×C11⋊(C11⋊(D19⋊C3)) |
| unambiguous semidirect product | (C2×C11)⋊(C11⋊(D19⋊C3)) |
| unambiguous semidirect product | (C2×C19⋊C3)⋊(C11⋊D11) |
| Fitting, socle | C2×C112×C19 ⋊ C2×C3 |
| derived, Hall | C112×C19 ⋊ C22×C3 |
| Hall | C2×C11⋊D209 ⋊ C3 |
| Hall | C112×C19⋊C3 ⋊ C22 |
| Sylow | C112 ⋊ C2×D19⋊C3 |
| Hall | C19⋊C3 ⋊ C2×C11⋊D11 |
| Sylow | C19 ⋊ C2×C3×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊(C11⋊(D19⋊C3)) |
| commutator, cosocle, hypocenter | C112×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C19 | C2×C3 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 ◁ C2 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4598 |
1098 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27588, 94);