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D5×ΓL(1,𝔽8)×C11⋊C5 #26040480

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

Aliases

direct productD5×ΓL(1,𝔽8)×C11⋊C5
unambiguous semidirect productC5⋊(C2×ΓL(1,𝔽8)×C11⋊C5)
unambiguous semidirect product(C7×D5)⋊(C3×C11⋊C5)
unambiguous semidirect product(D5×C11)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(D5×C11×ΓL(1,𝔽8))⋊C5
unambiguous semidirect product(C7×D5×C11⋊C5)⋊C3

Splittings

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

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)⋊((C11⋊C5)⋊AGL(1,𝔽5)), C11⋊C5×ΓL(1,𝔽8)⋊AGL(1,𝔽5), ΓL(1,𝔽8)×(C11⋊C5)⋊AGL(1,𝔽5), …
maximal normal subgroup ofΓL(1,𝔽8)⋊((C11⋊C5)⋊AGL(1,𝔽5)), C11⋊C5×ΓL(1,𝔽8)⋊AGL(1,𝔽5), ΓL(1,𝔽8)×(C11⋊C5)⋊AGL(1,𝔽5), …
maximal quotient ofDic5×ΓL(1,𝔽8)×C11⋊C5, C2×D5×ΓL(1,𝔽8)×C11⋊C5, D5×C11⋊C5×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 44);