Finite Group DatabasebetaFinite Group Databasebeta| order | 22148 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×#90673⋊C7 |
| unambiguous semidirect product | #90673⋊C72 |
| unambiguous semidirect product | (C7×#90673)⋊C7 |
| Fitting, socle | C7×C113 ⋊ C4×C7 |
| derived, Sylow | C113 ⋊ C4×C72 |
| Hall | C7×C113⋊C7 ⋊ C4 |
| Hall | #90673 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #90673⋊C7 |
| commutator, hypocenter | C113 | C4×C72 |
| Frattini | C1 | G |
| Fitting, socle | C7×C113 | C4×C7 |
| prime radical | C7×D113⋊C7 | C2 |
| cosocle | D113 | C2×C72 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 791 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22148, 28);