Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #68000 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#68000 |
| derived | #95⋊C3 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #4626 |
| commutator, hypocenter | #95⋊C3 | C3×C4 |
| Frattini | C22×C4 | C3×S4 |
| Fitting | C3×#392 | D3 |
| socle | C23×C3 | SL(2,ℤ/4) |
| prime radical | C3×#392⋊C3 | C2 |
| cosocle | #392⋊C3 | C2×C3 |
| LCS | G ▷ #95⋊C3 | |
| UCS | C1 ◁ C2×C3 | |
150 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
63 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154132);