Finite Group DatabasebetaFinite Group Databasebeta| order | 22308 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#14523151 |
| Fitting, socle, Hall | C11×C132 ⋊ C3×C4 |
| derived, Sylow | C132 ⋊ C3×C4×C11 |
| Hall | C11×#10621729 ⋊ C3 |
| Hall | C11×C13×C13⋊C3 ⋊ C4 |
| Hall | #10621729 ⋊ C3×C11 |
| Hall | C13×C13⋊C3 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #14523151 |
| commutator, hypocenter | C132 | C3×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C132 | C3×C4 |
| prime radical | C11×(C13⋊C3)⋊D13 | C2 |
| cosocle | C13⋊D13 | C2×C3×C11 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C11 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 858 |
374 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22308, 80);