Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of Dic42 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊Dic21 |
| Hall | C3×C7 ⋊ C2×C4⋊C4 |
| Sylow | C7 ⋊ C2×C4⋊Dic3 |
| Sylow | C3 ⋊ C2×C4⋊Dic7 |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #13051008, #13051009, #13051015, … |
| maximal normal subgroup of | #13051008, #13051009, #13051015, … |
| maximal quotient of | C2×C4⋊(C3⋊(C7⋊C8)), #13056561, C4×C4⋊Dic21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 990);