Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of D7×D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C5×C72 ⋊ C2×C4 |
| Sylow | C72 ⋊ C4×D5 |
| Sylow | C5 ⋊ #87639 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×D35 |
| commutator, hypocenter | C5×C72 | C2×C4 |
| Fitting, socle, cosocle | C2×C5×C72 | C22 |
| prime radical | C2×C5⋊(C7⋊D7) | C2 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C2 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
Polycyclic presentation:
2^3,5,7^2|a^2=c,b^2=c,d^a=d^4,e^a=e^6,f^b=f^6190 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#87639, #72243393, #72243408, … |
| maximal normal subgroup of | D5×#87639, #72243393, #72243408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 74);