Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #4621 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×SL(2,ℤ/8) |
| derived | #95⋊C3 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #857 |
| commutator, hypocenter | #95⋊C3 | C3×C4 |
| Frattini | C24 | C3×S4 |
| Fitting | C2×C3×#95 | D3 |
| socle | C24×C3 | S4 |
| prime radical | C2×C3×#95⋊C3 | C2 |
| cosocle | C2×#95⋊C3 | C2×C3 |
| LCS | G ▷ #95⋊C3 | |
| UCS | C1 ◁ C22×C3 | |
224 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154128);