Finite Group Databasebeta

← Prev (#46856034) Next (#46856036) →

C3×ΓL(1,𝔽8)⋊C4×C139 #46856035

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

Aliases

direct productC3×ΓL(1,𝔽8)⋊C4×C139
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C4×C139)
unambiguous semidirect productDic7⋊(C32×C139)
unambiguous semidirect product(C3×Dic7)⋊(C3×C139)

Splittings

derived, SylowC7 ⋊ C32×C4×C139
HallC3×ΓL(1,𝔽8)×C139 ⋊ C4
HallDic7×C139 ⋊ C32
HallC7×C139 ⋊ C32×C4
HallC3×ΓL(1,𝔽8) ⋊ C4×C139
HallDic7 ⋊ C32×C139

Subgroups

subgroupG/H
center, hypercenterC2×C3×C139AGL(1,𝔽7)
commutator, hypocenterC7C32×C4×C139
FrattiniC2C3×AGL(1,𝔽7)×C139
Fitting, socleC2×C3×C7×C139C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C139C2
cosocleC2×C7C2×C32×C139
LCSG ▷ C7
UCSC1 ◁ C2×C3×C139

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11676

Conjugacy classes & character table

5838 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35028, 71);