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C2×C5×C13×AGL(1,𝔽7) #19129785

order5460
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C13×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C2×C3×C5×C13)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C5×C13)
unambiguous semidirect product(C2×D7)⋊(C3×C5×C13)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C5×C13)
unambiguous semidirect product(C2×C5×D7)⋊(C3×C13)

Splittings

Fitting, socleC2×C5×C7×C13 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C5×C13
HallC2×C5×C13×D7 ⋊ C3
HallC5×C13×ΓL(1,𝔽8) ⋊ C22
HallC5×C7×C13 ⋊ C22×C3
HallC2×C13×D7 ⋊ C3×C5
HallC13×ΓL(1,𝔽8) ⋊ C22×C5
HallC2×C5×D7 ⋊ C3×C13
HallC5×ΓL(1,𝔽8) ⋊ C22×C13
HallC7×C13 ⋊ C22×C3×C5
HallC5×C7 ⋊ C22×C3×C13
HallC2×D7 ⋊ C3×C5×C13
HallΓL(1,𝔽8) ⋊ C22×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13AGL(1,𝔽7)
commutator, hypocenterC7C22×C3×C5×C13
FrattiniC1G
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C5×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

910 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×C13⋊C3×AGL(1,𝔽7), C5×D3×C13×AGL(1,𝔽7), C2×C3×C5×C13×AGL(1,𝔽7), …
maximal normal subgroup ofC2×C5×C13⋊C3×AGL(1,𝔽7), C2×C3×C5×C13×AGL(1,𝔽7), C2×C13×C25×AGL(1,𝔽7), …
maximal quotient ofC2×C5×C13×D7⋊C9, C5×D3×C13×AGL(1,𝔽7), C2×C3×C5×C13×AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 127);