Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C3×C8 |
| direct product | C82×C3⋊D3 |
| Fitting | C32×C82 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C82 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C82 |
| Frattini | C42 | C22×C3⋊D3 |
| Fitting | C32×C82 | C2 |
| socle | C22×C32 | C2×C42 |
| prime radical | C22×C3⋊D3 | C42 |
| cosocle | C32×C42 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C82 | |
840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×#1455, C3⋊D3×#1712, C3⋊D3×#1705, … |
| maximal normal subgroup of | C3⋊D3×#1455, C3⋊D3×#1712, C3⋊D3×#1705, … |
| maximal quotient of | C3⋊D3×#1311 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7502);