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C11×ΓL(1,𝔽8)×D25 #26040466

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

Aliases

direct productC11×ΓL(1,𝔽8)×D25
unambiguous semidirect productC25⋊(C2×C11×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D25)⋊(C3×C11)
unambiguous semidirect product(C7×C11×D25)⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×D25
commutator, cosocle, hypocenterC7×C25C2×C3×C11
FrattiniC5D5×C11×ΓL(1,𝔽8)
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

770 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×ΓL(1,𝔽8)⋊#1035, C11⋊(ΓL(1,𝔽8)⋊#1035), C11×ΓL(1,𝔽8)×#1035, …
maximal normal subgroup ofC11×ΓL(1,𝔽8)⋊#1035, C11⋊(ΓL(1,𝔽8)⋊#1035), C11×ΓL(1,𝔽8)×#1035, …
maximal quotient ofC11×ΓL(1,𝔽8)×Dic25, C2×C11×ΓL(1,𝔽8)×D25, C11×D25×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 30);