Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of C3⋊D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×C3⋊D21 |
| Fitting, socle | C23×C32×C7 ⋊ C2 |
| derived, Hall | C32×C7 ⋊ C24 |
| Sylow | C32 ⋊ C23×D7 |
| Sylow | C7 ⋊ C23×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊D21 |
| commutator, cosocle, hypocenter | C32×C7 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C32×C7 | C2 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C23 | |
804 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4×C3⋊D21, C23×D7×C3⋊D3, C2×#11759581, … |
| maximal normal subgroup of | C2×D4×C3⋊D21, C23×D7×C3⋊D3, C2×#11759581, … |
| maximal quotient of | C2×D4×C3⋊D21, C24×C3⋊D21, C22×D3×C3⋊D21 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 953);