Finite Group Databasebeta

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C2×C11×C5⋊(C7⋊D7) #24924792

order10780
isoclinismisoclinic class of C5⋊(C7⋊D7)
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C7

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C11C5⋊(C7⋊D7)
commutator, cosocle, hypocenterC5×C72C22×C11
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2
LCSG ▷ C5×C72
UCSC1 ◁ C2×C11

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C5⋊(ΓL(1,𝔽8)⋊D7), C2×C11×C5⋊#64424, C2×C11×C5⋊#64425, …
maximal normal subgroup ofC2×C11×C5⋊(ΓL(1,𝔽8)⋊D7), C2×C11×C5⋊#64424, C2×C11×C5⋊#64425, …
maximal quotient ofD3×C11×C5⋊(C7⋊D7), C2×C3×C11×C5⋊(C7⋊D7), C2×C11×C3⋊(C5⋊(C7⋊D7))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 105);