Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #3688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×#63422 |
| derived | Q8⋊C9 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | (C22⋊C9)⋊C2 |
| commutator, hypocenter | Q8⋊C9 | C22×C4 |
| Frattini | C3×C4 | C22×S4 |
| Fitting, prime radical | C22×C3×#41 | D3 |
| socle | C23×C3 | SL(2,ℤ/4) |
| cosocle | #41⋊C9 | C23 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C22×C4 | |
653 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 653 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154419);