Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #10588305 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#10588305 |
| derived | C22⋊(C22⋊C9) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10588305 |
| commutator, hypocenter | C22⋊(C22⋊C9) | C2×C4 |
| Frattini | C23×C3 | C2×S4 |
| Fitting, prime radical | C2×C3×#120 | D3 |
| socle | C23×C3 | SL(2,ℤ/4) |
| cosocle | #120⋊C9 | C22 |
| LCS | G ▷ C22⋊(C22⋊C9) | |
| UCS | C1 ◁ C2 | |
256 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
42 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154046);