Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#19153445 |
| Fitting, socle | C2×C312 ⋊ C2×C3 |
| derived, Sylow | C312 ⋊ C22×C3 |
| Hall | C2×C31×D31 ⋊ C3 |
| Hall | #15668332 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19153445 |
| commutator, cosocle, hypocenter | C312 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C312 | C2×C3 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C2 | |
100 conjugacy classes of subgroups.
362 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#19153449⋊C3, C2×C31⋊C3×D31⋊C3, D3×#19153445, … |
| maximal normal subgroup of | C2×C31⋊C3×D31⋊C3, C2×C3×#19153445 |
| maximal quotient of | C2×#31772346, D3×#19153445, C2×C3×#19153445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 43);