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C5×ΓL(1,𝔽8)⋊D53 #26013286

order11130
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)⋊D53
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D53)
unambiguous semidirect productC53⋊(C5×AGL(1,𝔽7))
unambiguous semidirect productD371⋊(C3×C5)
unambiguous semidirect product(C5×D371)⋊C3

Splittings

Fitting, socle, HallC5×C7×C53 ⋊ C2×C3
derived, HallC7×C53 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C53 ⋊ C2
HallC5×D371 ⋊ C3
HallΓL(1,𝔽8)×C53 ⋊ C2×C5
HallD371 ⋊ C3×C5
HallC5×C53 ⋊ AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ D53
SylowC53 ⋊ C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C3×D53
HallΓL(1,𝔽8) ⋊ C5×D53
SylowC7 ⋊ C3×C5×D53

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)⋊D53
commutator, cosocle, hypocenterC7×C53C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C53C2×C3
LCSG ▷ C7×C53
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

685 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D53, D5×ΓL(1,𝔽8)⋊D53, (C5⋊AGL(1,𝔽7))⋊D53, …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D53, D5×ΓL(1,𝔽8)⋊D53, (C5⋊AGL(1,𝔽7))⋊D53, …
maximal quotient ofC5×ΓL(1,𝔽8)⋊Dic53, C2×C5×ΓL(1,𝔽8)⋊D53, C5×C53⋊(D7⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11130, 20);