Finite Group DatabasebetaFinite Group Databasebeta| order | 18228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×#17986954 |
| Fitting, socle, Hall | C22×C72×C31 ⋊ C3 |
| derived, Hall | C72×C31 ⋊ C22×C3 |
| Hall | C22×C72 ⋊ C31⋊C3 |
| Hall | C22×C31 ⋊ #3861 |
| Sylow | C72 ⋊ C22×C31⋊C3 |
| Sylow | C31 ⋊ C22×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #17986954 |
| commutator, cosocle, hypocenter | C72×C31 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C31 | C3 |
| LCS | G ▷ C72×C31 | |
| UCS | C1 ◁ C22 | |
200 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, 306);