Finite Group DatabasebetaFinite Group Databasebeta| order | 12180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D435 |
| unambiguous semidirect product | (C3×D7)⋊D145 |
| unambiguous semidirect product | (C5×D7)⋊D87 |
| unambiguous semidirect product | (D7×C29)⋊D15 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C7×C29 | C22 |
| LCS | G ▷ C3×C5×C7×C29 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
1095 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D1305, AGL(1,𝔽7)×D435, C3×D7×D435, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D435, C3×D7×D435 |
| maximal quotient of | D7×D1305, C3×D7×D435, D21⋊D435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12180, 128);