Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221×C3 |
| direct product | C26×C3⋊D3 |
| Fitting, socle | C26×C32 ⋊ C2 |
| derived, Sylow | C32 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C27 |
| Frattini | C1 | G |
| Fitting, socle | C26×C32 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C26 | |
175272 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×#2846, C22×C3⋊D3×#120, C22×#10595527, … |
| maximal normal subgroup of | C3⋊D3×#2846, C22×C3⋊D3×#120, C22×#10595527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153310);