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C11×C23×AGL(1,𝔽7) #24922322

order10626
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC11×C23×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C11×C23)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C11×C23)
unambiguous semidirect product(C11×D7)⋊(C3×C23)
unambiguous semidirect product(C11×D7×C23)⋊C3

Splittings

Fitting, socle, HallC7×C11×C23 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C11×C23
HallC11×ΓL(1,𝔽8)×C23 ⋊ C2
HallC11×D7×C23 ⋊ C3
HallΓL(1,𝔽8)×C23 ⋊ C2×C11
HallD7×C23 ⋊ C3×C11
HallC11×ΓL(1,𝔽8) ⋊ C2×C23
HallC7×C23 ⋊ C2×C3×C11
HallC11×D7 ⋊ C3×C23
HallC7×C11 ⋊ C2×C3×C23
HallΓL(1,𝔽8) ⋊ C2×C11×C23
HallD7 ⋊ C3×C11×C23

Subgroups

subgroupG/H
center, hypercenterC11×C23AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C11×C23
FrattiniC1G
Fitting, socleC7×C11×C23C2×C3
LCSG ▷ C7
UCSC1 ◁ C11×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1771 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×AGL(1,𝔽7)×D23, D11×C23×AGL(1,𝔽7), AGL(1,𝔽7)×D253, …
maximal normal subgroup ofC11×AGL(1,𝔽7)×D23, D11×C23×AGL(1,𝔽7), AGL(1,𝔽7)×D253, …
maximal quotient ofC11×C23×ΓL(1,𝔽8)⋊C4, C2×C11×C23×AGL(1,𝔽7), C11×C23×D7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 30);