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C13×ΓL(1,𝔽8)×D35 #34062166

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)×D35
unambiguous semidirect productC5⋊(C13×D7×ΓL(1,𝔽8))

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derived, HallC5×C72 ⋊ C2×C3×C13
HallC5×C7×C13×ΓL(1,𝔽8) ⋊ C2
HallC7×C13×D35 ⋊ C3
HallC7×C13×ΓL(1,𝔽8) ⋊ D5
HallC5×C7×ΓL(1,𝔽8) ⋊ C2×C13
HallC72×C13 ⋊ C3×D5
HallC7×D35 ⋊ C3×C13
HallC7×ΓL(1,𝔽8) ⋊ D5×C13
HallC5×C13 ⋊ D7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×D5×C13
SylowC5 ⋊ C13×D7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC13ΓL(1,𝔽8)×D35
commutator, cosocle, hypocenterC5×C72C2×C3×C13
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C13

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

1235 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×AGL(1,𝔽7)×D35, D35×ΓL(1,𝔽8)⋊D13, C13×(C5⋊AGL(1,𝔽7))⋊D7, …
maximal normal subgroup ofC13×AGL(1,𝔽7)×D35, D35×ΓL(1,𝔽8)⋊D13, C13×(C5⋊AGL(1,𝔽7))⋊D7, …
maximal quotient ofC13×ΓL(1,𝔽8)×Dic35, C2×C13×ΓL(1,𝔽8)×D35

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 159);