Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #10624306 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, Hall | C32×C5 ⋊ C4⋊C4 |
| Sylow | C32 ⋊ C4⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ #3773 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator | C5×C3⋊D3 | C2×C4 |
| Fitting, socle, hypocenter | C32×C5 | C4⋊C4 |
| prime radical, cosocle | D5×C3⋊D3 | C22 |
| LCS | G ▷ C5×C3⋊D3 ▷ C32×C5 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
Polycyclic presentation:
2^4,3^2,5|a^2=c,b^2=d,b^a=bd,e^a=f,f^a=e,g^a=g^3,e^b=f^2,f^b=e,g^c=g^4,e^d=e^2,f^d=f^224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 775);