Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | A4×#953 |
| Fitting | C26×C3 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×A4 |
| commutator, socle, cosocle | C24×C3 | C23×C3 |
| Fitting | C26×C3 | C2×C3 |
| hypercenter | C24 | D3×A4 |
| hypocenter | C22×C3 | C3×#120 |
| LCS | G ▷ C24×C3 ▷ C22×C3 | |
| UCS | C1 ◁ C22 ◁ C24 | |
2082 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 2082 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#64269, D3×A4×#120, #72242491, … |
| maximal normal subgroup of | D3×A4×#120, #72242491, C3×A4×#953 |
| maximal quotient of | C3×A4×#953 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157422);