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C7×C11×(C5⋊D5)⋊C3 #26040512

order11550
isoclinismisoclinic class of (C5⋊D5)⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C5

Aliases

direct productC7×C11×(C5⋊D5)⋊C3
unambiguous semidirect product(C5⋊D5)⋊(C3×C7×C11)
unambiguous semidirect product(C11×C5⋊D5)⋊(C3×C7)

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C2×C3
derived, SylowC52 ⋊ C2×C3×C7×C11
HallC7×C11×C52⋊C3 ⋊ C2
HallC7×C11×C5⋊D5 ⋊ C3
HallC11×C52⋊C3 ⋊ C2×C7
HallC11×C5⋊D5 ⋊ C3×C7
HallC7×C52⋊C3 ⋊ C2×C11
HallC7×C5⋊D5 ⋊ C3×C11
HallC52×C11 ⋊ C2×C3×C7
HallC52×C7 ⋊ C2×C3×C11
HallC52⋊C3 ⋊ C2×C7×C11
HallC5⋊D5 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC7×C11(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52C2×C3×C7×C11
FrattiniC1G
Fitting, socleC52×C7×C11C2×C3
LCSG ▷ C52
UCSC1 ◁ C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

770 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C11×#3874⋊C2, C7×((C5⋊D5)⋊C3)⋊D11, C11×((C5⋊D5)⋊C3)⋊D7, …
maximal normal subgroup ofC7×C11×#3874⋊C2, C7×((C5⋊D5)⋊C3)⋊D11, C11×((C5⋊D5)⋊C3)⋊D7, …
maximal quotient ofC7×C11×#1039⋊C3, C2×C7×C11×(C5⋊D5)⋊C3, C7×C11×(C5⋊D5)⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 76);