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C7×C11⋊((C5⋊D5)⋊C3) #26040513

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C5

Aliases

direct productC7×C11⋊((C5⋊D5)⋊C3)
unambiguous semidirect productC11⋊(C7×(C5⋊D5)⋊C3)
unambiguous semidirect product(C5⋊D55)⋊(C3×C7)

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C2×C3
derived, HallC52×C11 ⋊ C2×C3×C7
HallC7×C11×C52⋊C3 ⋊ C2
HallC7×C5⋊D55 ⋊ C3
HallC11×C52⋊C3 ⋊ C2×C7
HallC5⋊D55 ⋊ C3×C7
HallC7×C52⋊C3 ⋊ D11
HallC52×C7 ⋊ C3×D11
HallC7×C11 ⋊ (C5⋊D5)⋊C3
HallC52⋊C3 ⋊ C7×D11
SylowC52 ⋊ C3×C7×D11
SylowC11 ⋊ C7×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C11⋊((C5⋊D5)⋊C3)
commutator, cosocle, hypocenterC52×C11C2×C3×C7
FrattiniC1G
Fitting, socleC52×C7×C11C2×C3
LCSG ▷ C52×C11
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

455 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×#3874⋊D11, #37528481, C7×D11×(C5⋊D5)⋊C3, …
maximal normal subgroup ofC7×#3874⋊D11, #37528481, C7×D11×(C5⋊D5)⋊C3, …
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, 77);