Finite Group Databasebeta

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C2×C7×C13×D35 #27164973

order12740
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C22×C7×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C13×D35
unambiguous semidirect product(C2×C5)⋊(C7×C13×D7)
unambiguous semidirect product(C2×C7)⋊(C7×D5×C13)

Splittings

Fitting, socleC2×C5×C72×C13 ⋊ C2
derivedC5×C7 ⋊ C22×C7×C13
HallC5×C72×C13 ⋊ C22
HallC72×C13 ⋊ C2×D5
HallC5×C72 ⋊ C22×C13
HallC5×C13 ⋊ C2×C7×D7
SylowC72 ⋊ C2×D5×C13
SylowC5 ⋊ C2×C7×C13×D7

Subgroups

subgroupG/H
center, hypercenterC2×C7×C13D35
commutator, cosocle, hypocenterC5×C7C22×C7×C13
FrattiniC1G
Fitting, socleC2×C5×C72×C13C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C7×C13

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3458 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C13×C5⋊#64418, C2×C7×C13×C5⋊AGL(1,𝔽7), C2×C7×C5⋊#10587720, …
maximal normal subgroup ofC2×C7×C13×C5⋊AGL(1,𝔽7), C2×C7×C5⋊#10587720, C2×C7×C5⋊#10587721, …
maximal quotient ofD3×C7×C13×D35, C2×C3×C7×C13×D35, C2×C7×C13×D105

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12740, 103);