Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #4380 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived, Hall | C32×C5 ⋊ C16 |
| Sylow | C32 ⋊ #674 |
| Sylow | C5 ⋊ #3708 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #4380 |
| commutator, hypocenter | C32×C5 | C16 |
| Fitting | C32×C4×C5 | C4 |
| socle, prime radical | C2×C32×C5 | C8 |
| cosocle | C3⋊(C3⋊#168) | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C4 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^4,3^2,5|a^2=b,b^2=c,c^2=d,e^a=ef,f^a=ef^2,g^a=g^2,e^b=e^2,f^b=f^2,g^b=g^460 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#3708, #13085540, #13085541, … |
| maximal normal subgroup of | D5⋊#3708, #13085540, #13085541, … |
| maximal quotient of | #13084631, C2×#10623725 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 194);