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C11×ΓL(1,𝔽8)×D41 #34038826

order18942
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)×D41
unambiguous semidirect productC41⋊(C2×C11×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D41)⋊(C3×C11)
unambiguous semidirect product(C7×C11×D41)⋊C3

Splittings

Fitting, socle, HallC7×C11×C41 ⋊ C2×C3
derived, HallC7×C41 ⋊ C2×C3×C11
HallC11×ΓL(1,𝔽8)×C41 ⋊ C2
HallC7×C11×D41 ⋊ C3
HallΓL(1,𝔽8)×C41 ⋊ C2×C11
HallC7×D41 ⋊ C3×C11
HallC11×C41 ⋊ C2×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×D41
SylowC41 ⋊ C2×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11×D41

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×D41
commutator, cosocle, hypocenterC7×C41C2×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C41C2×C3
LCSG ▷ C7×C41
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3157

Conjugacy classes & character table

1210 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×ΓL(1,𝔽8)⋊#4223, C11×AGL(1,𝔽7)×D41, C11⋊(ΓL(1,𝔽8)⋊#4223), …
maximal normal subgroup ofC11×ΓL(1,𝔽8)⋊#4223, C11×AGL(1,𝔽7)×D41, C11⋊(ΓL(1,𝔽8)⋊#4223), …
maximal quotient ofC11×ΓL(1,𝔽8)×Dic41, C2×C11×ΓL(1,𝔽8)×D41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18942, 18);