Finite Group DatabasebetaFinite Group Databasebeta| order | 18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D653 |
| unambiguous semidirect product | C653⋊(C22×C7) |
| unambiguous semidirect product | (C2×C653)⋊(C2×C7) |
| Fitting, socle | C2×C7×C653 ⋊ C2 |
| derived, Sylow | C653 ⋊ C22×C7 |
| Hall | C7×C653 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D653 |
| commutator, cosocle, hypocenter | C653 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C653 | C2 |
| LCS | G ▷ C653 | |
| UCS | C1 ◁ C2×C7 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9142 |
4592 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18284, 11);