Finite Group DatabasebetaFinite Group Databasebeta| order | 18228 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#14579595 |
| derived | C7×C31 ⋊ C3×C4×C7 |
| Hall | C72×Dic31 ⋊ C3 |
| Hall | C7×#10620252 ⋊ C4 |
| Hall | C72×C31 ⋊ C3×C4 |
| Hall | Dic31 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ (C31⋊C3)⋊C4 |
| Sylow | C31 ⋊ C4×C7×ΓL(1,𝔽8) |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2604 |
630 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18228, 73);