Finite Group DatabasebetaFinite Group Databasebeta| order | 18228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×#17986945 |
| Fitting, Hall | C22×C31×C49 ⋊ C3 |
| derived, Hall | C31×C49 ⋊ C22×C3 |
| Hall | C22×C49 ⋊ C31⋊C3 |
| Hall | C22×C31 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ C22×C31⋊C3 |
| Sylow | C31 ⋊ C22×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #17986945 |
| commutator, cosocle, hypocenter | C31×C49 | C22×C3 |
| Frattini | C7 | C22×#10620252 |
| Fitting | C22×C31×C49 | C3 |
| socle | C22×C7×C31 | ΓL(1,𝔽8) |
| LCS | G ▷ C31×C49 | |
| UCS | C1 ◁ C22 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6076 |
2036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18228, 51);