Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #92722 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C4⋊(C3⋊D21) |
| Fitting | C2×C32×C4×C7 ⋊ C2 |
| Hall | C32×C7 ⋊ C2×D4 |
| Sylow | C32 ⋊ C2×D28 |
| Sylow | C7 ⋊ C2×C4⋊(C3⋊D3) |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
258 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3⋊D3×D28, C2×D4×C3⋊D21, C2×D7×C4⋊(C3⋊D3), … |
| maximal normal subgroup of | C2×C3⋊D3×D28, C2×D4×C3⋊D21, C2×D7×C4⋊(C3⋊D3), … |
| maximal quotient of | #72246361, #72246766 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 868);