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C3×(C41⋊C5)⋊D11 #27214281

order13530
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C41⋊C5)⋊D11
unambiguous semidirect product(C41⋊C5)⋊(C3×D11)

Splittings

Fitting, socle, HallC3×C11×C41 ⋊ C2×C5
derived, HallC11×C41 ⋊ C2×C3×C5
HallC3×C11×C41⋊C5 ⋊ C2
HallC3×D451 ⋊ C5
HallC11×C41⋊C5 ⋊ C2×C3
HallD451 ⋊ C3×C5
HallC3×C41⋊C5 ⋊ D11
HallC41⋊C5 ⋊ C3×D11
HallC3×C41 ⋊ C5×D11
SylowC41 ⋊ C3×C5×D11
HallC3×C11 ⋊ D41⋊C5
SylowC11 ⋊ C3×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC3(C41⋊C5)⋊D11
commutator, cosocle, hypocenterC11×C41C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C41C2×C5
LCSG ▷ C11×C41
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 1353

A minimal faithful permutation representation — 2 generators on 55 points:

(2,6,7,23,27,3,4,12,14,22)(5,19,20,25,26,9,10,34,13,36)(8,31,32,33,21,16,17,41,18,11)(15,38,39,24,37,29,30,40,28,35)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54,55);(1,2,5,11,22,34,37,41,36,25,4,8,18,31,39,38,14,28,7,15,10,19,29,12,24,23,30,40,17,33,16,6,13,26,32,35,20,27,21,9,3)(42,43,45,47,49,51,52,50,48,46,44)

Conjugacy classes & character table

237 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D11×D41⋊C5, D3×(C41⋊C5)⋊D11, (C3⋊(D41⋊C5))⋊D11, …
maximal normal subgroup ofC3×D11×D41⋊C5, D3×(C41⋊C5)⋊D11, (C3⋊(D41⋊C5))⋊D11, …
maximal quotient ofC3×#22583156, C2×C3×(C41⋊C5)⋊D11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13530, 35);