Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #5450 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C3×#5450 |
| Fitting | C2×C3×H(3,𝔽4) ⋊ C3 |
| derived | C24 ⋊ C23×C32 |
| Sylow | C2×H(3,𝔽4) ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #5450 |
| commutator, cosocle, hypocenter | C24 | C23×C32 |
| Frattini | C22 | C23×C3×A4 |
| Fitting | C2×C3×H(3,𝔽4) | C3 |
| socle | C23×C3 | C22×A4 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C2×C3 | |
736 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11921058, C2×A4×#5450, C2×C3×#4625⋊C2, … |
| maximal normal subgroup of | C2×#11921058, C2×C3×#4625⋊C2, C2×C3×#5450⋊C3 |
| maximal quotient of | C2×A4×#5450, C2×C3×#11709314 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153783);