Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D32×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D32×D7 |
| unambiguous semidirect product | (C3×D3×D7)⋊C22 |
| unambiguous semidirect product | (D7×C3⋊D3)⋊C22 |
| unambiguous semidirect product | (D3×D21)⋊C22 |
| Fitting, socle | C2×C32×C7 ⋊ C23 |
| derived, Hall | C32×C7 ⋊ C24 |
| Sylow | C32 ⋊ C23×D7 |
| Sylow | C7 ⋊ C22×D32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D32×D7 |
| commutator, cosocle, hypocenter | C32×C7 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C7 | C23 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C2 | |
568 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 84 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D32×AGL(1,𝔽7), C4×D32×D7, C2×D7×GO+(4,𝔽2), … |
| maximal normal subgroup of | C2×D32×AGL(1,𝔽7), C4×D32×D7, C2×D7×GO+(4,𝔽2), … |
| maximal quotient of | C4×D32×D7, D32×D5×D7, D7×#3811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 922);