Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C31 |
No aliases for this group.
| derived, Sylow | C312 ⋊ C3×C4 |
| Hall | C31⋊Dic31 ⋊ C3 |
| Hall | #15668333 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19153444 |
| commutator, hypocenter | C312 | C3×C4 |
| Fitting, socle, cosocle | C2×C312 | C2×C3 |
| prime radical | C2×#15668333 | C2 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C2 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,31^2,2|a^2=e,c^a=c^30,d^a=d^30,c^b=c^5,d^b=d^25332 conjugacy classes — view the full character table.
| maximal subgroup of | (C31⋊C3)⋊((C31⋊C3)⋊C4), C3×#26040336, C3⋊#26040336 |
| maximal normal subgroup of | (C31⋊C3)⋊((C31⋊C3)⋊C4), C3×#26040336 |
| maximal quotient of | #46829290, C3×#26040336, C3⋊#26040336 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 19);