Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #126⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C22×C3×#126⋊C3 |
| Fitting | C22×C3×#126 ⋊ C3 |
| derived | C42 ⋊ C23×C32 |
| Sylow | C22×#126 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #126⋊C3 |
| commutator, cosocle, hypocenter | C42 | C23×C32 |
| Frattini | C22 | C23×C3×A4 |
| Fitting | C22×C3×#126 | C3 |
| socle | C24×C3 | C2×A4 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C22×C3 | |
696 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153715);