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C2×C5⋊(C7⋊D77) #24924791

order10780
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C5⋊(C7⋊D77)
unambiguous semidirect product(C2×C5)⋊(C7⋊D77)
unambiguous semidirect product(C2×C7)⋊D385
unambiguous semidirect product(C2×C11)⋊(C5⋊(C7⋊D7))

Splittings

Fitting, socleC2×C5×C72×C11 ⋊ C2
derived, HallC5×C72×C11 ⋊ C22
HallC72×C11 ⋊ C2×D5
HallC5×C72 ⋊ C2×D11
HallC5×C11 ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×D55
SylowC11 ⋊ C2×C5⋊(C7⋊D7)
SylowC5 ⋊ C2×C7⋊D77

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C7⋊D77)
commutator, cosocle, hypocenterC5×C72×C11C22
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2
LCSG ▷ C5×C72×C11
UCSC1 ◁ C2

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2698 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊(C11⋊(ΓL(1,𝔽8)⋊D7)), C2×C5⋊(C11⋊#64424), C2×C5⋊(C11⋊#64425), …
maximal normal subgroup ofC2×C5⋊(C11⋊(ΓL(1,𝔽8)⋊D7)), C2×C5⋊(C11⋊#64424), C2×C5⋊(C11⋊#64425), …
maximal quotient ofD3×C5⋊(C7⋊D77), C2×C3×C5⋊(C7⋊D77), C2×C3⋊(C5⋊(C7⋊D77))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 104);