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C11×C5⋊(C5⋊AGL(1,𝔽7)) #26040504

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C5

Aliases

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

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C2×C3
derived, HallC52×C7 ⋊ C2×C3×C11
HallC52×C11×ΓL(1,𝔽8) ⋊ C2
HallC11×C5⋊D35 ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ C2×C11
HallC5⋊D35 ⋊ C3×C11
HallC52×C11 ⋊ AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ C5⋊D5
HallC7×C11 ⋊ C3×C5⋊D5
SylowC52 ⋊ C11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C11×C5⋊D5
SylowC7 ⋊ C3×C11×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC11C5⋊(C5⋊AGL(1,𝔽7))
commutator, cosocle, hypocenterC52×C7C2×C3×C11
FrattiniC1G
Fitting, socleC52×C7×C11C2×C3
LCSG ▷ C52×C7
UCSC1 ◁ C11

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

737 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C11×C5⋊AGL(1,𝔽7), D55⋊(C5⋊AGL(1,𝔽7)), D11×C5⋊(C5⋊AGL(1,𝔽7)), …
maximal normal subgroup ofD5×C11×C5⋊AGL(1,𝔽7), D55⋊(C5⋊AGL(1,𝔽7)), D11×C5⋊(C5⋊AGL(1,𝔽7)), …
maximal quotient ofC11×ΓL(1,𝔽8)⋊#1039, 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, 68);