Finite Group DatabasebetaFinite Group Databasebeta| order | 18326 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C7 |
| direct product | C11×C7⋊D119 |
| unambiguous semidirect product | C7⋊(C11×D119) |
| unambiguous semidirect product | C17⋊(C11×C7⋊D7) |
| Fitting, socle, Hall | C72×C11×C17 ⋊ C2 |
| derived, Hall | C72×C17 ⋊ C2×C11 |
| Hall | C72×C11 ⋊ D17 |
| Hall | C11×C17 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C11×D17 |
| Sylow | C17 ⋊ C11×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C7⋊D119 |
| commutator, cosocle, hypocenter | C72×C17 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11×C17 | C2 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C11 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9163 |
4598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#16809725, C11⋊#16809725, C11×D7×D119, … |
| maximal normal subgroup of | C11×#16809725, C11⋊#16809725, C11×D7×D119, … |
| maximal quotient of | C11×C7⋊Dic119, C2×C11×C7⋊D119 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18326, 12);