Finite Group DatabasebetaFinite Group Databasebeta| order | 22372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17×C47 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic7×C47 |
| unambiguous semidirect product | C7⋊(C4×C17×C47) |
| derived, Sylow | C7 ⋊ C4×C17×C47 |
| Hall | C7×C17×C47 ⋊ C4 |
| Hall | C7×C47 ⋊ C4×C17 |
| Hall | C7×C17 ⋊ C4×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17×C47 | D7 |
| commutator, hypocenter | C7 | C4×C17×C47 |
| Frattini | C2 | D7×C17×C47 |
| Fitting, socle, prime radical | C2×C7×C17×C47 | C2 |
| cosocle | C2×C7 | C2×C17×C47 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C17×C47 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22372 |
7990 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22372, 5);