Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C24×C3×D7 |
| Fitting, socle | C24×C3×C7 ⋊ C2 |
| derived, Sylow | C7 ⋊ C25×C3 |
| Hall | C3×C7 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C3 | D7 |
| commutator, cosocle, hypocenter | C7 | C25×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3×C7 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C24×C3 | |
1496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | #13054862, C3×#89727, C22×(C2×D7)⋊Dic3, … |
| maximal normal subgroup of | #13054862, C3×#89727, C22×(C2×D7)⋊Dic3, … |
| maximal quotient of | C23×C3×Dic14, C23×C3×C4×D7, C23×C3×D28, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1277);