Finite Group DatabasebetaFinite Group Databasebeta| order | 22428 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×C7×#67063 |
| Fitting, socle, Hall | C32×C7×C89 ⋊ C4 |
| derived, Sylow | C89 ⋊ C32×C4×C7 |
| Hall | C32×C89 ⋊ C4×C7 |
| Hall | C7×C89 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C7 | #67063 |
| commutator, hypocenter | C89 | C32×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C89 | C4 |
| prime radical | C32×C7×D89 | C2 |
| cosocle | D89 | C2×C32×C7 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C32×C7 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5607 |
1638 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22428, 87);