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D11×C11⋊AGL(1,𝔽7) #23779017

order10164
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD11×C11⋊AGL(1,𝔽7)
unambiguous semidirect product(C11×D11)⋊AGL(1,𝔽7)
unambiguous semidirect product(ΓL(1,𝔽8)×D11)⋊D11
unambiguous semidirect product(D11×D77)⋊C3

Splittings

Fitting, socle, derived, HallC7×C112 ⋊ C22×C3
HallD11×D77 ⋊ C3
HallC112×ΓL(1,𝔽8) ⋊ C22
SylowC112 ⋊ C2×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ D112
SylowC7 ⋊ C3×D112

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C112C22×C3
LCSG ▷ C7×C112
UCSC1

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10624391⋊AGL(1,𝔽7), C3×D11×C11⋊AGL(1,𝔽7), D11×C3⋊(C11⋊AGL(1,𝔽7)), …
maximal normal subgroup ofC3×D11×C11⋊AGL(1,𝔽7)
maximal quotient ofD11×C11⋊(D7⋊C9), C3×D11×C11⋊AGL(1,𝔽7), D11×C3⋊(C11⋊AGL(1,𝔽7)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10164, 69);