Finite Group DatabasebetaFinite Group Databasebeta| order | 28322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72×C17 · Schur multiplier (H2) = C7 |
| direct product | C72×C17×D17 |
| unambiguous semidirect product | C17⋊(C2×C72×C17) |
| Fitting, socle, Hall | C72×C172 ⋊ C2 |
| derived | C17 ⋊ C2×C72×C17 |
| Sylow | C172 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72×C17 | D17 |
| commutator, cosocle, hypocenter | C17 | C2×C72×C17 |
| Frattini | C1 | G |
| Fitting, socle | C72×C172 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C72×C17 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1666 |
8330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28322, 18);