Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of C3⋊D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| derived, Hall | C32×C5 ⋊ C2×C8 |
| Sylow | C32 ⋊ D5⋊C8 |
| Sylow | C5 ⋊ C8×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D3×AGL(1,𝔽5) |
| commutator, hypocenter | C32×C5 | C2×C8 |
| Fitting, socle | C2×C32×C5 | C2×C4 |
| prime radical | C2×C3⋊D15 | C4 |
| cosocle | C32×Dic5 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3^2,5|a^2=c,b^2=d,c^2=d,g^a=g^2,e^b=e^2,f^b=f^2,g^c=g^460 conjugacy classes — view the full character table.
| maximal subgroup of | #13088343, #13088346, D3×#6738, … |
| maximal normal subgroup of | #13088343, #13088346, D3×#6738, … |
| maximal quotient of | #13085428, #13085430, C3⋊Dic3×#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 436);