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C5×AGL(1,𝔽7)×C53 #26013285

order11130
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C53 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽7)×C53
unambiguous semidirect productD7⋊(C3×C5×C53)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C5×C53)
unambiguous semidirect product(C5×D7)⋊(C3×C53)
unambiguous semidirect product(D7×C53)⋊(C3×C5)
unambiguous semidirect product(C5×D7×C53)⋊C3

Splittings

Fitting, socle, HallC5×C7×C53 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C5×C53
HallC5×ΓL(1,𝔽8)×C53 ⋊ C2
HallC5×D7×C53 ⋊ C3
HallΓL(1,𝔽8)×C53 ⋊ C2×C5
HallD7×C53 ⋊ C3×C5
HallC7×C53 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8) ⋊ C2×C53
HallC5×D7 ⋊ C3×C53
HallC5×C7 ⋊ C2×C3×C53
HallΓL(1,𝔽8) ⋊ C2×C5×C53
HallD7 ⋊ C3×C5×C53

Subgroups

subgroupG/H
center, hypercenterC5×C53AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C5×C53
FrattiniC1G
Fitting, socleC5×C7×C53C2×C3
LCSG ▷ C7
UCSC1 ◁ C5×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1855 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D53, D5×AGL(1,𝔽7)×C53, AGL(1,𝔽7)×D265, …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D53, D5×AGL(1,𝔽7)×C53, AGL(1,𝔽7)×D265, …
maximal quotient ofC5×C53×ΓL(1,𝔽8)⋊C4, C2×C5×AGL(1,𝔽7)×C53, C5×C53×D7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11130, 19);