Finite Group Databasebeta

← Prev (#26013288) Next (#26013290) →

C53×C5⋊AGL(1,𝔽7) #26013289

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

Aliases

direct productC53×C5⋊AGL(1,𝔽7)
unambiguous semidirect productC5⋊(AGL(1,𝔽7)×C53)
unambiguous semidirect productΓL(1,𝔽8)⋊(D5×C53)
unambiguous semidirect productD35⋊(C3×C53)
unambiguous semidirect product(C53×D35)⋊C3

Splittings

Fitting, socle, HallC5×C7×C53 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C53
HallC5×ΓL(1,𝔽8)×C53 ⋊ C2
HallC53×D35 ⋊ C3
HallΓL(1,𝔽8)×C53 ⋊ D5
HallC7×C53 ⋊ C3×D5
HallC5×C53 ⋊ AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×C53
HallD35 ⋊ C3×C53
HallΓL(1,𝔽8) ⋊ D5×C53
SylowC7 ⋊ C3×D5×C53
SylowC5 ⋊ AGL(1,𝔽7)×C53

Subgroups

subgroupG/H
center, hypercenterC53C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C2×C3×C53
FrattiniC1G
Fitting, socleC5×C7×C53C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C53

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

901 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD53×C5⋊AGL(1,𝔽7), D5×AGL(1,𝔽7)×C53, (C5⋊AGL(1,𝔽7))⋊D53, …
maximal normal subgroup ofD53×C5⋊AGL(1,𝔽7), D5×AGL(1,𝔽7)×C53, (C5⋊AGL(1,𝔽7))⋊D53, …
maximal quotient ofC53×ΓL(1,𝔽8)⋊Dic5, C2×C53×C5⋊AGL(1,𝔽7), C53×C5⋊(D7⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11130, 23);