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C11×ΓL(1,𝔽8)⋊D25 #26040468

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)⋊D25
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×D25)
unambiguous semidirect productC25⋊(C11×AGL(1,𝔽7))
unambiguous semidirect productD175⋊(C3×C11)
unambiguous semidirect product(C11×D175)⋊C3

Splittings

Fitting, HallC7×C11×C25 ⋊ C2×C3
derived, HallC7×C25 ⋊ C2×C3×C11
HallC11×ΓL(1,𝔽8)×C25 ⋊ C2
HallC11×D175 ⋊ C3
HallΓL(1,𝔽8)×C25 ⋊ C2×C11
HallD175 ⋊ C3×C11
HallC11×C25 ⋊ AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ D25
HallC7×C11 ⋊ C3×D25
SylowC25 ⋊ C11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C11×D25
SylowC7 ⋊ C3×C11×D25

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)⋊D25
commutator, cosocle, hypocenterC7×C25C2×C3×C11
FrattiniC5C11×C5⋊AGL(1,𝔽7)
FittingC7×C11×C25C2×C3
socleC5×C7×C11C3×D5
LCSG ▷ C7×C25
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

737 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×ΓL(1,𝔽8)⋊D25, C11×AGL(1,𝔽7)×D25, (C11⋊AGL(1,𝔽7))⋊D25, …
maximal normal subgroup ofD11×ΓL(1,𝔽8)⋊D25, C11×AGL(1,𝔽7)×D25, (C11⋊AGL(1,𝔽7))⋊D25, …
maximal quotient ofC11×ΓL(1,𝔽8)⋊Dic25, C2×C11×ΓL(1,𝔽8)⋊D25, C11×C25⋊(D7⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 32);