Finite Group DatabasebetaFinite Group Databasebeta| order | 18228 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic217 |
| derived, Hall | C72×C31 ⋊ C3×C4 |
| Hall | C7×Dic217 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8)×C31 ⋊ C4 |
| Hall | C7×ΓL(1,𝔽8) ⋊ Dic31 |
| Sylow | C72 ⋊ C3×Dic31 |
| Sylow | C31 ⋊ ΓL(1,𝔽8)×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)×D217 |
| commutator, hypocenter | C72×C31 | C3×C4 |
| Fitting, socle, cosocle | C2×C72×C31 | C2×C3 |
| prime radical | C2×C7×ΓL(1,𝔽8)×C31 | C2 |
| LCS | G ▷ C72×C31 | |
| UCS | C1 ◁ C2 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2604 |
1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18228, 116);