Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of C3⋊D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C4×C3⋊D21 |
| Fitting | C2×C32×C4×C7 ⋊ C2 |
| derived, Hall | C32×C7 ⋊ C22×C4 |
| Sylow | C32 ⋊ C2×C4×D7 |
| Sylow | C7 ⋊ C2×C4×C3⋊D3 |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C4×D7×C3⋊D3, C2×D4×C3⋊D21, C2×#11759568, … |
| maximal normal subgroup of | C2×C4×D7×C3⋊D3, C2×D4×C3⋊D21, C2×#11759568, … |
| maximal quotient of | C42×C3⋊D21, C22⋊C4×C3⋊D21 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 867);