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C5×AGL(1,𝔽7)×C139 #44415916

order29190
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C139 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽7)×C139
unambiguous semidirect productD7⋊(C3×C5×C139)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C5×C139)
unambiguous semidirect product(C5×D7)⋊(C3×C139)

Splittings

Fitting, socle, HallC5×C7×C139 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C5×C139
HallC5×ΓL(1,𝔽8)×C139 ⋊ C2
HallC5×D7×C139 ⋊ C3
HallΓL(1,𝔽8)×C139 ⋊ C2×C5
HallD7×C139 ⋊ C3×C5
HallC7×C139 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8) ⋊ C2×C139
HallC5×D7 ⋊ C3×C139
HallC5×C7 ⋊ C2×C3×C139
HallΓL(1,𝔽8) ⋊ C2×C5×C139
HallD7 ⋊ C3×C5×C139

Subgroups

subgroupG/H
center, hypercenterC5×C139AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C5×C139
FrattiniC1G
Fitting, socleC5×C7×C139C2×C3
LCSG ▷ C7
UCSC1 ◁ C5×C139

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4865

Conjugacy classes & character table

4865 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29190, 26);