Finite Group Databasebeta

← Prev (#20301898) Next (#20301900) →

C2×C53×D35 #20301899

order7420
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C22×C53 · Schur multiplier (H2) = C2

Aliases

direct productC2×C53×D35
unambiguous semidirect product(C2×C5)⋊(D7×C53)
unambiguous semidirect product(C2×C7)⋊(D5×C53)

Splittings

Fitting, socleC2×C5×C7×C53 ⋊ C2
derived, HallC5×C7 ⋊ C22×C53
HallC5×C7×C53 ⋊ C22
HallC7×C53 ⋊ C2×D5
HallC5×C53 ⋊ C2×D7
SylowC7 ⋊ C2×D5×C53
SylowC5 ⋊ C2×D7×C53

Subgroups

subgroupG/H
center, hypercenterC2×C53D35
commutator, hypocenterC5×C7C22×C53
FrattiniC1G
Fitting, socleC2×C5×C7×C53C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C53

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2014 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C53×C5⋊AGL(1,𝔽7), D3×C53×D35, C2×C3×C53×D35, …
maximal normal subgroup ofC2×C53×C5⋊AGL(1,𝔽7), C2×C3×C53×D35, C2×C5×C53×D35
maximal quotient ofD3×C53×D35, C2×C3×C53×D35, C2×C53×D105, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7420, 30);