Finite Group Databasebeta

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C2×C7×C11×D35 #24924794

order10780
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C22×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C11×D35
unambiguous semidirect product(C2×C5)⋊(C7×C11×D7)
unambiguous semidirect product(C2×C7)⋊(C7×D5×C11)

Splittings

Fitting, socleC2×C5×C72×C11 ⋊ C2
derivedC5×C7 ⋊ C22×C7×C11
HallC5×C72×C11 ⋊ C22
HallC72×C11 ⋊ C2×D5
HallC5×C72 ⋊ C22×C11
HallC5×C11 ⋊ C2×C7×D7
SylowC72 ⋊ C2×D5×C11
SylowC5 ⋊ C2×C7×C11×D7

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11D35
commutator, cosocle, hypocenterC5×C7C22×C7×C11
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C7×C11

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2926 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C5⋊#64418, C2×C7×C11×C5⋊AGL(1,𝔽7), C2×C11×ΓL(1,𝔽8)×D35, …
maximal normal subgroup ofC2×C7×C11×C5⋊AGL(1,𝔽7), C2×C11×ΓL(1,𝔽8)×D35, C2×C11×C5⋊#64423, …
maximal quotient ofD3×C7×C11×D35, C2×C3×C7×C11×D35, C2×C7×C11×D105

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 107);