Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×#1020⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | D3×#1020⋊C2 |
| unambiguous semidirect product | #10593244⋊C2 |
| unambiguous semidirect product | (D3×#1020)⋊C2 |
| Fitting | C3×#120 ⋊ C2×D3 |
| derived | C3×C22⋊A4 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C22⋊A4 | C23 |
| Frattini | C22 | C2×D3×S4 |
| Fitting | C3×#120 | C2×D3 |
| socle | C22×C3 | C22×S4 |
| LCS | G ▷ C3×C22⋊A4 | |
| UCS | C1 | |
945 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 945 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(3,𝔽2), #72210357, D3×#11715753, … |
| maximal normal subgroup of | C3×D3×#1020⋊C2, C2×D3×#1020⋊C2, D3×#4625⋊C2 |
| maximal quotient of | #72210357, C3×D3×#1020⋊C2, D3×#10593244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155790);