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C3×C4×ΓL(1,𝔽8)×C139 #46856064

order35028
automorphism?
homologyAbelianization (H1) = C32×C4×C139 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×ΓL(1,𝔽8)×C139
unambiguous semidirect product(C4×C7)⋊(C32×C139)
unambiguous semidirect product(C3×C4×C7)⋊(C3×C139)

Splittings

FittingC3×C4×C7×C139 ⋊ C3
derived, SylowC7 ⋊ C32×C4×C139
HallC4×C7×C139 ⋊ C32
HallC7×C139 ⋊ C32×C4
HallC4×C7 ⋊ C32×C139

Subgroups

subgroupG/H
center, hypercenterC3×C4×C139ΓL(1,𝔽8)
commutator, hypocenterC7C32×C4×C139
FrattiniC2C2×C3×ΓL(1,𝔽8)×C139
FittingC3×C4×C7×C139C3
socleC2×C3×C7×C139C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C139C2
cosocleC2×C7C2×C32×C139
LCSG ▷ C7
UCSC1 ◁ C3×C4×C139

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11676

Conjugacy classes & character table

8340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35028, 100);