Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#3773 |
| Hall | C32×C7 ⋊ C4⋊C4 |
| Sylow | C32 ⋊ C7×C4⋊C4 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#3773, C4×C7×GO+(4,𝔽2), #72217839, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×#3773, C4×C7×GO+(4,𝔽2), #72217839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 567);