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C4×ΓL(1,𝔽8)×C139 #26043002

order11676
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C4×C139 · Schur multiplier (H2) = C1

Aliases

direct productC4×ΓL(1,𝔽8)×C139
unambiguous semidirect product(C4×C7)⋊(C3×C139)

Splittings

Fitting, HallC4×C7×C139 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C139
HallC7×C139 ⋊ C3×C4
HallC4×C7 ⋊ C3×C139

Subgroups

subgroupG/H
center, hypercenterC4×C139ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C139
FrattiniC2C2×ΓL(1,𝔽8)×C139
FittingC4×C7×C139C3
socleC2×C7×C139C2×C3
prime radicalC2×ΓL(1,𝔽8)×C139C2
cosocleC2×C7C2×C3×C139
LCSG ▷ C7
UCSC1 ◁ C4×C139

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2780 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×ΓL(1,𝔽8)×C139⋊C3, Dic3×ΓL(1,𝔽8)×C139, C3×C4×ΓL(1,𝔽8)×C139
maximal normal subgroup ofC4×ΓL(1,𝔽8)×C139⋊C3, C3×C4×ΓL(1,𝔽8)×C139
maximal quotient ofC4×C7⋊C9×C139, Dic3×ΓL(1,𝔽8)×C139, C3×C4×ΓL(1,𝔽8)×C139

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11676, 3);