Finite Group DatabasebetaFinite Group Databasebeta| order | 18486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D1027 |
| Fitting, socle, Hall | C32×C13×C79 ⋊ C2 |
| derived, Hall | C13×C79 ⋊ C2×C32 |
| Hall | C32×C79 ⋊ D13 |
| Hall | C32×C13 ⋊ D79 |
| Sylow | C79 ⋊ C32×D13 |
| Sylow | C13 ⋊ C32×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D1027 |
| commutator, cosocle, hypocenter | C13×C79 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C79 | C2 |
| LCS | G ▷ C13×C79 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9243 |
4635 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D13×D79, C3×D3×D1027, C3×D39⋊D79, … |
| maximal normal subgroup of | C32×D13×D79, C3×D3×D1027, C3×D39⋊D79, … |
| maximal quotient of | C32×Dic1027, C2×C32×D1027 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18486, 86);