Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C72 ⋊ Q8 |
| Sylow | C72 ⋊ Dic10 |
| Sylow | C5 ⋊ #87642 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×D35 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C5×C72 | C22 |
| hypocenter | C5×C72 | Q8 |
| LCS | G ▷ C2×C5×C72 ▷ C5×C72 | |
| UCS | C1 ◁ C2 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^3,5,7^2|a^2=c,b^2=c,b^a=bc,d^a=d^4,e^a=e^6,f^b=f^6187 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 78);