Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#67×S4 |
| Fitting | C25×C3 ⋊ C2×D3 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D3×S4 |
| commutator, cosocle | C2×C3×A4 | C24 |
| Frattini | C2 | C22×D3×S4 |
| Fitting | C25×C3 | C2×D3 |
| socle | C24×C3 | C22×D3 |
| hypercenter | C23 | D3×S4 |
| hypocenter | C3×A4 | C22×D4 |
| LCS | G ▷ C2×C3×A4 ▷ C3×A4 | |
| UCS | C1 ◁ C22 ◁ C23 | |
2644 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 2644 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C2×S4×C3⋊S4, D3×#67×S4, #72242491, … |
| maximal normal subgroup of | #72242491, C2×D3×D4×S4, #72252962, … |
| maximal quotient of | D3×#67×S4, #72242450, #72242491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157639);