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C11×C3⋊(D41⋊C5) #27214293

order13530
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(D41⋊C5)
unambiguous semidirect productC3⋊(C11×D41⋊C5)
unambiguous semidirect product(C41⋊C5)⋊(D3×C11)
unambiguous semidirect productD123⋊(C5×C11)

Splittings

Fitting, socle, HallC3×C11×C41 ⋊ C2×C5
derived, HallC3×C41 ⋊ C2×C5×C11
HallC3×C11×C41⋊C5 ⋊ C2
HallC11×D123 ⋊ C5
HallC11×C41⋊C5 ⋊ D3
HallC3×C41⋊C5 ⋊ C2×C11
HallC11×C41 ⋊ C5×D3
HallD123 ⋊ C5×C11
HallC41⋊C5 ⋊ D3×C11
SylowC41 ⋊ C5×D3×C11
HallC3×C11 ⋊ D41⋊C5
SylowC3 ⋊ C11×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(D41⋊C5)
commutator, cosocle, hypocenterC3×C41C2×C5×C11
FrattiniC1G
Fitting, socleC3×C11×C41C2×C5
LCSG ▷ C3×C41
UCSC1 ◁ C11

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:

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

Conjugacy classes & character table

297 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C11×D41⋊C5, D11×C3⋊(D41⋊C5), (C3⋊(D41⋊C5))⋊D11, …
maximal normal subgroup ofD3×C11×D41⋊C5, D11×C3⋊(D41⋊C5), (C3⋊(D41⋊C5))⋊D11, …
maximal quotient ofC11×C3⋊(Dic41⋊C5), C2×C11×C3⋊(D41⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13530, 47);