Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #85559 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#85559 |
| Fitting | C3×H(3,𝔽4) ⋊ D3 |
| derived | #5464 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #85559 |
| commutator, cosocle, hypocenter | #5464 | C2×C3 |
| Frattini | C22 | C3×#1020 |
| Fitting | C3×H(3,𝔽4) | D3 |
| socle | C22×C3 | #1020 |
| LCS | G ▷ #5464 | |
| UCS | C1 ◁ C3 | |
256 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
36 conjugacy classes — view the full character table.
| maximal subgroup of | #72209735, C3×#11715753, D3×#85559, … |
| maximal normal subgroup of | C3×#11715753, D3×#85559, #72215235, … |
| maximal quotient of | C3×#11714279, C3×#11714262, C3×#11714256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157118);