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D3×C41×C11⋊C5 #27214288

order13530
automorphism?
homologyAbelianization (H1) = C2×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productD3×C41×C11⋊C5
unambiguous semidirect productC3⋊(C2×C41×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊(C5×C41)

Splittings

Fitting, socle, HallC3×C11×C41 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C41
HallC3×C41×C11⋊C5 ⋊ C2
HallD3×C11×C41 ⋊ C5
HallC11×C41 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ C2×C41
HallC3×C41 ⋊ C2×C11⋊C5
HallD3×C11 ⋊ C5×C41
SylowC11 ⋊ C5×D3×C41
SylowC3 ⋊ C2×C41×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC41D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C5×C41
FrattiniC1G
Fitting, socleC3×C11×C41C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C41

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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×C41×AGL(1,𝔽11), D3×(C11⋊C5)⋊D41, D3×C11⋊C5×D41, …
maximal normal subgroup ofD3×C41×AGL(1,𝔽11), D3×(C11⋊C5)⋊D41, D3×C11⋊C5×D41, …
maximal quotient ofDic3×C41×C11⋊C5, C2×D3×C41×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13530, 42);