Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×C22⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C29 |
| direct product | D3×C22⋊(C22⋊A4) |
| unambiguous semidirect product | C3⋊(C2×C22⋊(C22⋊A4)) |
| Fitting, socle, derived | C26×C3 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C26×C3 | C2×C3 |
| LCS | G ▷ C26×C3 | |
| UCS | C1 | |
19812 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#85645, D3×#87588, C2×D3×C22⋊(C22⋊A4) |
| maximal normal subgroup of | D3×#85645, D3×#87588, C2×D3×C22⋊(C22⋊A4) |
| maximal quotient of | D3×C22⋊#997, C2×D3×C22⋊(C22⋊A4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157877);