Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C32×D28 |
| Fitting | C2×C32×C4×C7 ⋊ C2 |
| Hall | C32×C7 ⋊ C2×D4 |
| Sylow | C7 ⋊ C2×C32×D4 |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3⋊D3×D28, C2×C32×D4×D7, C2×#11759568, … |
| maximal normal subgroup of | C2×C3⋊D3×D28, C2×C32×D4×D7, C2×#11759568, … |
| maximal quotient of | C32×#6437, C32×#6445 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 828);