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C2×C7×C7⋊AGL(1,𝔽11) #24924751

order10780
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C7⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C7)⋊(C7×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C7×D7)
unambiguous semidirect product(C2×D77)⋊(C5×C7)
unambiguous semidirect product(C2×C7×D77)⋊C5

Splittings

Fitting, socleC2×C72×C11 ⋊ C2×C5
derivedC7×C11 ⋊ C22×C5×C7
HallC72×C11⋊C5 ⋊ C22
HallC2×C7×D77 ⋊ C5
HallC72×C11 ⋊ C22×C5
HallC11⋊C5 ⋊ C2×C7×D7
SylowC72 ⋊ C2×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×C7×D7

Subgroups

subgroupG/H
center, hypercenterC2×C7C7⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C22×C5×C7
FrattiniC1G
Fitting, socleC2×C72×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C7

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

448 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C11⋊C5)⋊#64418, C2×C7×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C2×ΓL(1,𝔽8)×C7⋊AGL(1,𝔽11), …
maximal normal subgroup ofC2×C7×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C2×ΓL(1,𝔽8)×C7⋊AGL(1,𝔽11), C2×(C11⋊C5)⋊#64423, …
maximal quotient ofD3×C7×C7⋊AGL(1,𝔽11), C2×C3×C7×C7⋊AGL(1,𝔽11), C2×C7×C3⋊(C7⋊AGL(1,𝔽11))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 64);