Finite Group DatabasebetaFinite Group Databasebeta| order | 18396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| Fitting, socle | C3×C7×C73 ⋊ C22×C3 |
| derived | C3×C73 ⋊ C22×C3×C7 |
| Hall | C3×C7×C73⋊C3 ⋊ C22 |
| Hall | C3×C73⋊C3 ⋊ C22×C7 |
| Hall | C7×C73 ⋊ C2×C3×D3 |
| Sylow | C73 ⋊ C2×C3×D3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D3×D73⋊C3 |
| commutator, cosocle, hypocenter | C3×C73 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C73 | C22×C3 |
| LCS | G ▷ C3×C73 | |
| UCS | C1 ◁ C7 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1533 |
378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18396, 175);