Finite Group DatabasebetaFinite Group Databasebeta| order | 22372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C17 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C17×D47 |
| unambiguous semidirect product | C47⋊(C22×C7×C17) |
| unambiguous semidirect product | (C2×C47)⋊(C2×C7×C17) |
| Fitting, socle | C2×C7×C17×C47 ⋊ C2 |
| derived, Sylow | C47 ⋊ C22×C7×C17 |
| Hall | C7×C17×C47 ⋊ C22 |
| Hall | C17×C47 ⋊ C22×C7 |
| Hall | C7×C47 ⋊ C22×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C17 | D47 |
| commutator, cosocle, hypocenter | C47 | C22×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C17×C47 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C2×C7×C17 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11186 |
5950 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22372, 21);