Finite Group DatabasebetaFinite Group Databasebeta| order | 22372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D17×D47 |
| unambiguous semidirect product | (D17×C47)⋊(C2×C7) |
| unambiguous semidirect product | (C17×D47)⋊(C2×C7) |
| unambiguous semidirect product | D799⋊(C2×C7) |
| Fitting, socle, Hall | C7×C17×C47 ⋊ C22 |
| derived, Hall | C17×C47 ⋊ C22×C7 |
| Hall | C7×C47 ⋊ C2×D17 |
| Hall | C7×C17 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×C7×D17 |
| Sylow | C17 ⋊ C2×C7×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D17×D47 |
| commutator, cosocle, hypocenter | C17×C47 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C47 | C22 |
| LCS | G ▷ C17×C47 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5593 |
1750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22372, 12);