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C2×C5×ΓL(1,𝔽8)×C11⋊C5 #26040481

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC2×C5×ΓL(1,𝔽8)×C11⋊C5
unambiguous semidirect product(C2×C7)⋊(C3×C5×C11⋊C5)
unambiguous semidirect product(C2×C11)⋊(C52×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C5×C7)⋊(C3×C11⋊C5)
unambiguous semidirect product(C2×C5×C11)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C11×ΓL(1,𝔽8))⋊C52
unambiguous semidirect product(C2×C7×C11⋊C5)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C11×ΓL(1,𝔽8))⋊C5
unambiguous semidirect product(C2×C5×C7×C11⋊C5)⋊C3

Splittings

Fitting, socleC2×C5×C7×C11 ⋊ C3×C5
derived, HallC7×C11 ⋊ C2×C3×C52
HallC2×C5×C7×C11⋊C5 ⋊ C3
HallC5×C7×C11⋊C5 ⋊ C2×C3
HallC2×C11×ΓL(1,𝔽8) ⋊ C52
HallC11×ΓL(1,𝔽8) ⋊ C2×C52
HallC2×C7×C11 ⋊ C3×C52
HallC2×C11 ⋊ C52×ΓL(1,𝔽8)
HallC2×C7 ⋊ C3×C5×C11⋊C5
SylowC11 ⋊ C2×C52×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C3×C5×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)×C11⋊C5
commutator, cosocle, hypocenterC7×C11C2×C3×C52
FrattiniC1G
Fitting, socleC2×C5×C7×C11C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C5

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

350 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×ΓL(1,𝔽8)⋊(Dic11⋊C5), C5×C11⋊C5×ΓL(1,𝔽8)⋊C4, C5×ΓL(1,𝔽8)×Dic11⋊C5, …
maximal normal subgroup ofC5×ΓL(1,𝔽8)⋊(Dic11⋊C5), C5×C11⋊C5×ΓL(1,𝔽8)⋊C4, C5×ΓL(1,𝔽8)×Dic11⋊C5, …
maximal quotient ofC4×C5×ΓL(1,𝔽8)×C11⋊C5, C22×C5×ΓL(1,𝔽8)×C11⋊C5, C2×C5×C11⋊C5×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 45);