Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C31 |
No aliases for this group.
| Fitting, socle, Sylow | C312 ⋊ Dic3 |
| derived, Hall | #15668333 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | #15668333 | C4 |
| Fitting, socle | C312 | Dic3 |
| prime radical, cosocle | #19153444 | C2 |
| LCS | G ▷ #15668333 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,31^2|a^2=b,c^a=c^2,d^a=d^26e^5,e^a=de^5,d^b=d^30,e^b=e^30,d^c=d^25e^7,e^c=e^586 conjugacy classes — view the full character table.
| maximal subgroup of | #26040355⋊C3, C3×#26040355, C3⋊#26040355 |
| maximal normal subgroup of | #26040355⋊C3, C3×#26040355 |
| maximal quotient of | #46829309, C3×#26040355, C3⋊#26040355 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 38);