Finite Group Databasebeta

C7×Dic70 #14520002

order1960
isoclinismisoclinic class of Dic70
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic70

Splittings

HallC5×C72 ⋊ Q8
SylowC72 ⋊ Dic10
SylowC5 ⋊ C7×Dic14

Subgroups

subgroupG/H
centerC2×C7C2×D35
commutator, cosocleC2×C5×C7C22×C7
FrattiniC2C2×C7×D35
FittingC4×C5×C72C2
socle, prime radicalC2×C5×C72C22
hypercenterC4×C7D35
hypocenterC5×C7C7×Q8
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2×C7 ◁ C4×C7

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 280

Conjugacy classes & character table

511 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 99);