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C7×D7×AGL(1,𝔽11) #24924743

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

Aliases

direct productC7×D7×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C7×D7)
unambiguous semidirect product(D7×D11)⋊(C5×C7)
unambiguous semidirect product(C7×AGL(1,𝔽11))⋊(C2×C7)
unambiguous semidirect product(D7×C11⋊C5)⋊(C2×C7)
unambiguous semidirect product(C7⋊AGL(1,𝔽11))⋊(C2×C7)
unambiguous semidirect product(C7×D7×D11)⋊C5

Splittings

Fitting, socle, HallC72×C11 ⋊ C22×C5
derivedC7×C11 ⋊ C22×C5×C7
HallC72×C11⋊C5 ⋊ C22
HallC7×D7×D11 ⋊ C5
HallC11⋊C5 ⋊ C2×C7×D7
SylowC72 ⋊ C2×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×C7×D7

Subgroups

subgroupG/H
center, hypercenterC7D7×AGL(1,𝔽11)
commutator, cosocle, hypocenterC7×C11C22×C5×C7
FrattiniC1G
Fitting, socleC72×C11C22×C5
LCSG ▷ C7×C11
UCSC1 ◁ C7

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

385 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×#64418, C7×AGL(1,𝔽7)×AGL(1,𝔽11), D7×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal normal subgroup ofC7×AGL(1,𝔽7)×AGL(1,𝔽11), D7×ΓL(1,𝔽8)×AGL(1,𝔽11), AGL(1,𝔽11)×#64423, …
maximal quotient ofC3×C7×D7×AGL(1,𝔽11), C7×D21×AGL(1,𝔽11), C7×D7×C3⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 56);