Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×C7⋊C8 |
| derived, Sylow | C7 ⋊ C2×C32×C8 |
| Hall | C32×C7 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C4 | D7 |
| commutator, hypocenter | C7 | C2×C32×C8 |
| Frattini | C4 | C2×C32×D7 |
| Fitting | C2×C32×C4×C7 | C2 |
| socle, prime radical | C22×C32×C7 | C4 |
| cosocle | C4×C7 | C22×C32 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C32×C4 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1008 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 415);