Finite Group DatabasebetaFinite Group Databasebeta| order | 18516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C1543 ⋊ C2×C3 |
| derived, Sylow | C1543 ⋊ C22×C3 |
| Hall | C2×D1543 ⋊ C3 |
| Hall | C1543⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1543⋊C3 |
| commutator, cosocle, hypocenter | C1543 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1543 | C2×C3 |
| LCS | G ▷ C1543 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3086 |
526 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18516, 8);