Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×Dic21 |
| derived, Hall | C3×C7 ⋊ C23×C4 |
| Sylow | C7 ⋊ C23×Dic3 |
| Sylow | C3 ⋊ C23×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D21 |
| commutator, hypocenter | C3×C7 | C23×C4 |
| Frattini | C2 | C23×D21 |
| Fitting, socle, prime radical | C24×C3×C7 | C2 |
| cosocle | C2×C3×C7 | C24 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C24 | |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10620529, #13054851, #13054860, … |
| maximal normal subgroup of | C2×#10620529, #13054851, #13054860, … |
| maximal quotient of | C23×C3⋊(C7⋊C8), C22×#66627, C22×C4×Dic21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1246);