Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of #1132⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic28⋊C3 |
| unambiguous semidirect product | (C2×Dic28)⋊C3 |
| Hall | C2×Dic28 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×Q16 |
| Sylow | C7 ⋊ C2×C3×Q16 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | #89287⋊C3, #89291⋊C3, #89298⋊C3, … |
| maximal normal subgroup of | #89287⋊C3, #89291⋊C3, #89298⋊C3, … |
| maximal quotient of | #89453⋊C3, #89454⋊C3, C4×Dic28⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 323);