Finite Group DatabasebetaFinite Group Databasebeta| order | 18524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#13132997 |
| Fitting, socle, Hall | C11×C421 ⋊ C4 |
| derived, Sylow | C421 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #13132997 |
| commutator, hypocenter | C421 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C421 | C4 |
| prime radical | C11×D421 | C2 |
| cosocle | D421 | C2×C11 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4631 |
1199 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18524, 6);