Finite Group DatabasebetaFinite Group Databasebeta| order | 12012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D231 |
| unambiguous semidirect product | (C3×D13)⋊D77 |
| unambiguous semidirect product | (C7×D13)⋊D33 |
| unambiguous semidirect product | (C11×D13)⋊D21 |
| 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.
936 conjugacy classes — view the full character table.
| maximal subgroup of | D13×D693, #10587716⋊D33, #10587717⋊D33, … |
| maximal normal subgroup of | #10587716⋊D33, #10587717⋊D33, D13×C3⋊(C11⋊AGL(1,𝔽7)), … |
| maximal quotient of | D13×D693, C3×D13×D231, D39⋊D231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12012, 144);