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ΓL(1,𝔽8)×C5⋊AGL(1,𝔽11) #26040479

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C5⋊AGL(1,𝔽11)
unambiguous semidirect productC5⋊(ΓL(1,𝔽8)×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(D5×ΓL(1,𝔽8))
unambiguous semidirect productD55⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×D55)⋊C5
unambiguous semidirect product(C7×C5⋊AGL(1,𝔽11))⋊C3

Splittings

Fitting, socle, derivedC5×C7×C11 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallC7×C5⋊AGL(1,𝔽11) ⋊ C3
HallC5×C7×C11⋊C5 ⋊ C2×C3
HallC5×C11⋊C5 ⋊ C2×ΓL(1,𝔽8)
HallC11×ΓL(1,𝔽8) ⋊ C5×D5
HallC7×C11 ⋊ C3×C5×D5
SylowC11 ⋊ C5×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C11C2×C3×C5
LCSG ▷ C5×C7×C11
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×C5⋊AGL(1,𝔽11), (C5⋊AGL(1,𝔽7))⋊AGL(1,𝔽11), D5×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal normal subgroup ofAGL(1,𝔽7)×C5⋊AGL(1,𝔽11), (C5⋊AGL(1,𝔽7))⋊AGL(1,𝔽11), D5×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal quotient ofΓL(1,𝔽8)×(C11⋊C5)⋊Dic5, C2×ΓL(1,𝔽8)×C5⋊AGL(1,𝔽11), C7⋊C9×C5⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 43);