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C2×C7×C5⋊D35 #19096702

order4900
isoclinismisoclinic class of C5⋊D35
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C5

Aliases

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

Splittings

Fitting, socleC2×C52×C72 ⋊ C2
derivedC52×C7 ⋊ C22×C7
HallC52×C72 ⋊ C22
SylowC72 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×C7×D7

Subgroups

subgroupG/H
center, hypercenterC2×C7C5⋊D35
commutator, hypocenterC52×C7C22×C7
FrattiniC1G
Fitting, socleC2×C52×C72C2
LCSG ▷ C52×C7
UCSC1 ◁ C2×C7

208 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1246 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C5⋊(C5⋊AGL(1,𝔽7)), C2×C5⋊(C5⋊#64423), C2×C5⋊(C5⋊#64422), …
maximal normal subgroup ofC2×C7×C5⋊(C5⋊AGL(1,𝔽7)), C2×C5⋊(C5⋊#64423), C2×C5⋊(C5⋊#64422), …
maximal quotient ofD3×C7×C5⋊D35, C2×C7×C3⋊(C5⋊D35), C2×C3×C7×C5⋊D35

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4900, 106);