Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #67992 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#67992 |
| Fitting | C3×C82 ⋊ D3 |
| derived | C82⋊C3 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #67992 |
| commutator, cosocle, hypocenter | C82⋊C3 | C2×C3 |
| Frattini | C42 | C3×S4 |
| Fitting | C3×C82 | D3 |
| socle | C22×C3 | #857 |
| LCS | G ▷ C82⋊C3 | |
| UCS | C1 ◁ C3 | |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154124);