Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C31 |
| direct product | C2×#19153444 |
| Fitting, socle | C2×C312 ⋊ C2×C3 |
| derived, Sylow | C312 ⋊ C22×C3 |
| Hall | C2×C31⋊D31 ⋊ C3 |
| Hall | #15668333 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19153444 |
| commutator, cosocle, hypocenter | C312 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C312 | C2×C3 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C2 | |
90 conjugacy classes of subgroups.
332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 42);