Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of C3⋊(C3⋊(D7⋊A4)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C3⋊(C3⋊(D7⋊A4)) |
| unambiguous semidirect product | (C22⋊ΓL(1,𝔽8))⋊(C3⋊D3) |
| Fitting, socle, derived | C22×C32×C7 ⋊ C2×C3 |
| Sylow | C7 ⋊ A4×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C32×C7 | C2×C3 |
| LCS | G ▷ C22×C32×C7 | |
| UCS | C1 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
Polycyclic presentation:
2,3,2^2,3^2,7|e^a=e^2,f^a=f^2,g^a=g^6,c^b=d,d^b=cd,g^b=g^460 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 862);