Finite Group DatabasebetaFinite Group Databasebeta| order | 18228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D1519 |
| Fitting | C2×C3×C31×C49 ⋊ C2 |
| derived, Hall | C31×C49 ⋊ C22×C3 |
| Hall | C3×C31×C49 ⋊ C22 |
| Hall | C3×C49 ⋊ C2×D31 |
| Hall | C3×C31 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×C3×D31 |
| Sylow | C31 ⋊ C2×C3×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1519 |
| commutator, cosocle, hypocenter | C31×C49 | C22×C3 |
| Frattini | C7 | C2×C3×D217 |
| Fitting | C2×C3×C31×C49 | C2 |
| socle | C2×C3×C7×C31 | D7 |
| LCS | G ▷ C31×C49 | |
| UCS | C1 ◁ C2×C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9114 |
4566 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18228, 60);