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C41×C11⋊AGL(1,𝔽7) #34038831

order18942
automorphism?
homologyAbelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×C11⋊AGL(1,𝔽7)
unambiguous semidirect productC11⋊(C41×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(D11×C41)
unambiguous semidirect productD77⋊(C3×C41)
unambiguous semidirect product(C41×D77)⋊C3

Splittings

Fitting, socle, HallC7×C11×C41 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C41
HallC11×ΓL(1,𝔽8)×C41 ⋊ C2
HallC41×D77 ⋊ C3
HallΓL(1,𝔽8)×C41 ⋊ D11
HallC11×C41 ⋊ AGL(1,𝔽7)
HallC7×C41 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×C41
HallD77 ⋊ C3×C41
HallΓL(1,𝔽8) ⋊ D11×C41
SylowC11 ⋊ C41×AGL(1,𝔽7)
SylowC7 ⋊ C3×D11×C41

Subgroups

subgroupG/H
center, hypercenterC41C11⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C11C2×C3×C41
FrattiniC1G
Fitting, socleC7×C11×C41C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3157

Conjugacy classes & character table

1312 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD11×C41×AGL(1,𝔽7), (C11⋊AGL(1,𝔽7))⋊D41, D41×C11⋊AGL(1,𝔽7), …
maximal normal subgroup ofD11×C41×AGL(1,𝔽7), (C11⋊AGL(1,𝔽7))⋊D41, D41×C11⋊AGL(1,𝔽7), …
maximal quotient ofC41×C11⋊(ΓL(1,𝔽8)⋊C4), C2×C41×C11⋊AGL(1,𝔽7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18942, 23);