Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of #1141⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×#1144⋊C3 |
| unambiguous semidirect product | (C2×#1144)⋊C3 |
| Hall | C2×#1144 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×Q16 |
| Sylow | C7 ⋊ C2×C3×Q16 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | #89527⋊C3, #89565⋊C3, #89570⋊C3, … |
| maximal normal subgroup of | #89527⋊C3, #89565⋊C3, #89570⋊C3, … |
| maximal quotient of | #89742⋊C3, C2×#6381⋊C3, C2×#6384⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 361);