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C3×ΓL(1,𝔽8)×D139 #31776126

order17514
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×D139

Splittings

Fitting, socleC3×C7×C139 ⋊ C2×C3
derived, HallC7×C139 ⋊ C2×C32
HallC3×ΓL(1,𝔽8)×C139 ⋊ C2
HallC7×D139 ⋊ C32
SylowC139 ⋊ C2×C3×ΓL(1,𝔽8)
SylowC7 ⋊ C32×D139

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×D139
commutator, cosocle, hypocenterC7×C139C2×C32
FrattiniC1G
Fitting, socleC3×C7×C139C2×C3
LCSG ▷ C7×C139
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2919

Conjugacy classes & character table

1065 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×D139, C3⋊AGL(1,𝔽7)×D139, D3×ΓL(1,𝔽8)×D139, …
maximal normal subgroup ofC3×AGL(1,𝔽7)×D139, C3⋊AGL(1,𝔽7)×D139, D3×ΓL(1,𝔽8)×D139, …
maximal quotient ofC3×ΓL(1,𝔽8)×Dic139, C2×C3×ΓL(1,𝔽8)×D139

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17514, 39);