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C11⋊C5×C5⋊AGL(1,𝔽7) #26040478

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

Aliases

direct productC11⋊C5×C5⋊AGL(1,𝔽7)
unambiguous semidirect productC5⋊(AGL(1,𝔽7)×C11⋊C5)
unambiguous semidirect productΓL(1,𝔽8)⋊(D5×C11⋊C5)
unambiguous semidirect productD35⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×C5⋊AGL(1,𝔽7))⋊C5
unambiguous semidirect product(C11⋊C5×D35)⋊C3

Splittings

Fitting, socle, derivedC5×C7×C11 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallC11⋊C5×D35 ⋊ C3
HallC5×C7×C11⋊C5 ⋊ C2×C3
HallC5×C11⋊C5 ⋊ AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ C5×D5
HallC7×C11 ⋊ C3×C5×D5
HallΓL(1,𝔽8) ⋊ D5×C11⋊C5
SylowC11 ⋊ C5×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ C3×D5×C11⋊C5

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

119 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×C5⋊AGL(1,𝔽7), (C5⋊AGL(1,𝔽7))⋊AGL(1,𝔽11), D5×AGL(1,𝔽7)×C11⋊C5, …
maximal normal subgroup ofAGL(1,𝔽11)×C5⋊AGL(1,𝔽7), (C5⋊AGL(1,𝔽7))⋊AGL(1,𝔽11), D5×AGL(1,𝔽7)×C11⋊C5, …
maximal quotient ofC11⋊C5×ΓL(1,𝔽8)⋊Dic5, C2×C11⋊C5×C5⋊AGL(1,𝔽7), C11⋊C5×C5⋊(D7⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 42);