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C11×(C3⋊D3)⋊D5 #14520480

order1980
isoclinismisoclinic class of (C3⋊D3)⋊D5
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×(C3⋊D3)⋊D5
unambiguous semidirect product(C3⋊D3)⋊(D5×C11)
unambiguous semidirect productD15⋊(D3×C11)

Splittings

Fitting, socle, HallC32×C5×C11 ⋊ C22
derived, HallC32×C5 ⋊ C22×C11
HallC32×C11 ⋊ C2×D5
HallC5×C11 ⋊ D32
SylowC32 ⋊ C2×D5×C11
SylowC5 ⋊ D32×C11

Subgroups

subgroupG/H
center, hypercenterC11(C3⋊D3)⋊D5
commutator, cosocle, hypocenterC32×C5C22×C11
FrattiniC1G
Fitting, socleC32×C5×C11C22
LCSG ▷ C32×C5
UCSC1 ◁ C11

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 330

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(16,17)(18,19,21,22,20);(13,14)(15,16,17)(19,20)(21,22)

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C11×(C3⋊D3)⋊D5, C11×D15⋊D21, C11×(C3⋊D3)⋊D35, …
maximal normal subgroup ofC7×C11×(C3⋊D3)⋊D5, C121×(C3⋊D3)⋊D5, C112×(C3⋊D3)⋊D5, …
maximal quotient ofC7×C11×(C3⋊D3)⋊D5, C11×D15⋊D21, C11×(C3⋊D3)⋊D35, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 105);