Finite Group DatabasebetaFinite Group Databasebeta| order | 22148 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×Dic113⋊C7 |
| unambiguous semidirect product | Dic113⋊C72 |
| unambiguous semidirect product | (C7×Dic113)⋊C7 |
| derived, Sylow | C113 ⋊ C4×C72 |
| Hall | C7×C113⋊C7 ⋊ C4 |
| Hall | Dic113 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D113⋊C7 |
| commutator, hypocenter | C113 | C4×C72 |
| Frattini | C2 | C7×D113⋊C7 |
| Fitting, socle | C2×C7×C113 | C2×C7 |
| prime radical | C2×C7×C113⋊C7 | C2 |
| cosocle | C2×C113 | C2×C72 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C2×C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3164 |
308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22148, 18);