Finite Group DatabasebetaFinite Group Databasebeta| order | 12012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊D91 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C11×C13 | C22 |
| LCS | G ▷ C3×C7×C11×C13 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7,11,13|d^a=d^6,e^a=e^10,f^a=f^12,c^b=c^2,e^b=e^10831 conjugacy classes — view the full character table.
| maximal subgroup of | D99⋊D91, D33⋊#10587722, D33⋊#10587723, … |
| maximal normal subgroup of | D33⋊#10587722, D33⋊#10587723, D33⋊(ΓL(1,𝔽8)⋊D13), … |
| maximal quotient of | D99⋊D91, C3×D33⋊D91, D33⋊D273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12012, 163);