Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Hall | C32×C5 ⋊ C22⋊C4 |
| Sylow | C32 ⋊ #685 |
| Sylow | C5 ⋊ C22⋊#157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×#157 |
| commutator, Fitting, socle | C2×C32×C5 | C2×C4 |
| prime radical | C2×D5×C3⋊D3 | C2 |
| cosocle | C2×C5×C3⋊D3 | C22 |
| hypocenter | C32×C5 | C22⋊C4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^4,3^2,5|b^2=c,b^a=bd,g^a=g^4,e^b=f,f^b=e^2,e^c=e^2,f^c=f^242 conjugacy classes — view the full character table.
| maximal subgroup of | #13088446, #13088447, #13088455, … |
| maximal normal subgroup of | #13088446, #13088447, #13088455, … |
| maximal quotient of | #13085502, #13085503, #13085504, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 454);