Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #3774 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#3774 |
| Hall | C32×C7 ⋊ D8 |
| Sylow | C32 ⋊ C7×D8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | GO+(4,𝔽2) |
| commutator, cosocle | C3⋊Dic3 | C22×C7 |
| Frattini | C2 | C7×GO+(4,𝔽2) |
| Fitting, socle | C2×C32×C7 | D4 |
| hypocenter | C32 | C7×D8 |
| LCS | G ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C7 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 568);