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ΓL(1,𝔽8)×D11×C41 #34038827

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

Aliases

direct productΓL(1,𝔽8)×D11×C41
unambiguous semidirect productC11⋊(C2×ΓL(1,𝔽8)×C41)
unambiguous semidirect product(C7×D11)⋊(C3×C41)
unambiguous semidirect product(C7×D11×C41)⋊C3

Splittings

Fitting, socle, HallC7×C11×C41 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C41
HallC11×ΓL(1,𝔽8)×C41 ⋊ C2
HallC7×D11×C41 ⋊ C3
HallC11×C41 ⋊ C2×ΓL(1,𝔽8)
HallC7×C41 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×C41
HallC7×D11 ⋊ C3×C41
SylowC11 ⋊ C2×ΓL(1,𝔽8)×C41
SylowC7 ⋊ C3×D11×C41

Subgroups

subgroupG/H
center, hypercenterC41ΓL(1,𝔽8)×D11
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

1435 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD11×C41×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D41, ΓL(1,𝔽8)×D11×D41, …
maximal normal subgroup ofD11×C41×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D41, ΓL(1,𝔽8)×D11×D41, …
maximal quotient ofΓL(1,𝔽8)×C41×Dic11, C2×ΓL(1,𝔽8)×D11×C41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18942, 19);