Finite Group DatabasebetaFinite Group Databasebeta| order | 22372 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D119⋊D47 |
| unambiguous semidirect product | D329⋊D17 |
| unambiguous semidirect product | D799⋊D7 |
| Fitting, socle, derived, Hall | C7×C17×C47 ⋊ C22 |
| Hall | C17×C47 ⋊ C2×D7 |
| Hall | C7×C47 ⋊ C2×D17 |
| Hall | C7×C17 ⋊ C2×D47 |
| Sylow | C47 ⋊ D7×D17 |
| Sylow | C17 ⋊ D7×D47 |
| Sylow | C7 ⋊ D17×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C17×C47 | C22 |
| LCS | G ▷ C7×C17×C47 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5593 |
Polycyclic presentation:
2^2,7,17,47|d^a=d^16,e^a=e^46,c^b=c^6,d^b=d^161453 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22372, 20);