Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D7×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#92675 |
| derived, Hall | C32×C7 ⋊ C22×C4 |
| Sylow | C32 ⋊ C2×C4×D7 |
| Sylow | C7 ⋊ C2×C4×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D7×C3⋊D3 |
| commutator, hypocenter | C32×C7 | C22×C4 |
| Frattini | C2 | C2×D7×C3⋊D3 |
| Fitting, socle | C22×C32×C7 | C22 |
| prime radical | C22×C3⋊D21 | C2 |
| cosocle | C2×C32×C7 | C23 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C22 | |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×D7×C3⋊D3, C2×#11759581, C2×#13094713, … |
| maximal normal subgroup of | C2×C4×D7×C3⋊D3, C2×#11759581, C2×#13094713, … |
| maximal quotient of | C4×#92675, #72246726 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 745);