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C7×C5⋊(ΓL(1,𝔽8)⋊D13) #34062119

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C5⋊(ΓL(1,𝔽8)⋊D13)
unambiguous semidirect productC5⋊(C7×ΓL(1,𝔽8)⋊D13)
unambiguous semidirect productΓL(1,𝔽8)⋊(C7×D65)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derivedC5×C7×C13 ⋊ C2×C3×C7
HallC5×C7×C13×ΓL(1,𝔽8) ⋊ C2
HallC7×D455 ⋊ C3
HallC7×C13×ΓL(1,𝔽8) ⋊ D5
HallC5×C7×ΓL(1,𝔽8) ⋊ D13
HallC72×C13 ⋊ C3×D5
HallC5×C72 ⋊ C3×D13
HallC7×ΓL(1,𝔽8) ⋊ D65
HallC5×C13 ⋊ C7×AGL(1,𝔽7)
SylowC72 ⋊ C3×D65
SylowC13 ⋊ C7×C5⋊AGL(1,𝔽7)
SylowC5 ⋊ C7×ΓL(1,𝔽8)⋊D13

Subgroups

subgroupG/H
center, hypercenterC7C5⋊(ΓL(1,𝔽8)⋊D13)
commutator, cosocle, hypocenterC5×C7×C13C2×C3×C7
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C7

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

1169 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D13×C5⋊AGL(1,𝔽7), C7×AGL(1,𝔽7)×D65, C7×D5×ΓL(1,𝔽8)⋊D13, …
maximal normal subgroup ofC7×D13×C5⋊AGL(1,𝔽7), C7×AGL(1,𝔽7)×D65, C7×D5×ΓL(1,𝔽8)⋊D13, …
maximal quotient ofC7×ΓL(1,𝔽8)⋊Dic65, C2×C7×C5⋊(ΓL(1,𝔽8)⋊D13)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 112);