Finite Group DatabasebetaFinite Group Databasebeta| order | 12012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D39×D77 |
| 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.
840 conjugacy classes — view the full character table.
| maximal subgroup of | D77×D117, #49114737, #49114738, … |
| maximal normal subgroup of | #49114737, #49114738, D39×C11⋊AGL(1,𝔽7), … |
| maximal quotient of | D77×D117, C3×D39×D77, D39×D231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12012, 158);