Finite Group DatabasebetaFinite Group Databasebeta| order | 12180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C7⋊#10596816) |
| unambiguous semidirect product | C7⋊(C3⋊#10596816) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C7×C29 | C4 |
| LCS | G ▷ C3×C5×C7×C29 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,7,29|a^2=b,c^a=c^2,d^a=d^2,e^a=e^6,f^a=f^28,d^b=d^41221 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12180, 122);