Finite Group DatabasebetaFinite Group Databasebeta| order | 12012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D77⋊D39 |
| 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|c^a=c^2,e^a=e^10,f^a=f^12,d^b=d^6,e^b=e^10795 conjugacy classes — view the full character table.
| maximal subgroup of | D77⋊D117, #49114749, #49114750, … |
| maximal normal subgroup of | #49114749, #49114750, (C11⋊AGL(1,𝔽7))⋊D39, … |
| maximal quotient of | D77⋊D117, C3×D77⋊D39, #49114953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12012, 162);