Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #64188⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | C2×#64188⋊C2 |
| unambiguous semidirect product | #64188⋊C22 |
| derived | C22⋊(C22⋊C9) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #64188⋊C2 |
| commutator, cosocle, hypocenter | C22⋊(C22⋊C9) | C23 |
| Frattini | C22×C3 | C22×S4 |
| Fitting | C2×C3×#120 | D3 |
| socle | C23×C3 | C2×S4 |
| LCS | G ▷ C22⋊(C22⋊C9) | |
| UCS | C1 ◁ C2 | |
868 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 868 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154282);