Finite Group DatabasebetaFinite Group Databasebeta| order | 12180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D35⋊D87 |
| 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.
Polycyclic presentation:
2^2,3,5,7,29|c^a=c^2,e^a=e^6,f^a=f^28,d^b=d^4,e^b=e^6837 conjugacy classes — view the full character table.
| maximal subgroup of | D35⋊D261, (C5⋊AGL(1,𝔽7))⋊D87, C3×D35⋊D87, … |
| maximal normal subgroup of | (C5⋊AGL(1,𝔽7))⋊D87, C3×D35⋊D87 |
| maximal quotient of | D35⋊D261, C3×D35⋊D87, #49141615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12180, 144);