Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #3688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#3689 |
| derived | Q8⋊C9 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | (C22⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | Q8⋊C9 | C2×C7 |
| Frattini | C2×C3 | C7×S4 |
| Fitting | C3×C7×Q8 | D3 |
| socle | C2×C3×C7 | S4 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C2×C7 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 125);