Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C5×C72 ⋊ D4 |
| Sylow | C72 ⋊ C22⋊D5 |
| Sylow | C5 ⋊ #87641 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D35⋊D7 |
| commutator, Fitting, socle, cosocle | C2×C5×C72 | C22 |
| hypocenter | C5×C72 | D4 |
| LCS | G ▷ C2×C5×C72 ▷ C5×C72 | |
| UCS | C1 ◁ C2 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
Polycyclic presentation:
2^3,5,7^2|b^a=bc,d^a=d^4,e^a=e^6,e^b=e^6,f^b=f^6151 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#87641, #72243408, #72243410, … |
| maximal normal subgroup of | D5×#87641, #72243408, #72243410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 81);