Finite Group DatabasebetaFinite Group Databasebeta| order | 22148 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C22×C7×C113⋊C7 |
| unambiguous semidirect product | (C22×C113)⋊C72 |
| unambiguous semidirect product | (C22×C7×C113)⋊C7 |
| Fitting, socle | C22×C7×C113 ⋊ C7 |
| derived, Sylow | C113 ⋊ C22×C72 |
| Hall | C22×C113 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C7 | C113⋊C7 |
| commutator, cosocle, hypocenter | C113 | C22×C72 |
| Frattini | C1 | G |
| Fitting, socle | C22×C7×C113 | C7 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C22×C7 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3164 |
644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22148, 34);