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D3×#14555919 #27214289

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

Aliases

direct productD3×#14555919
unambiguous semidirect productC3⋊(C2×#14555919)

Splittings

Fitting, socle, derived, HallC3×C11×C41 ⋊ C2×C5
HallC3×#14555919 ⋊ C2
HallD3×C11×C41 ⋊ C5
HallC11×C41 ⋊ C5×D3
HallD3×C41 ⋊ C11⋊C5
HallC3×C41 ⋊ C2×C11⋊C5
HallD3×C11 ⋊ C41⋊C5
SylowC41 ⋊ D3×C11⋊C5
HallC3×C11 ⋊ C2×C41⋊C5
SylowC11 ⋊ D3×C41⋊C5
SylowC3 ⋊ C2×#14555919

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C41C2×C5
LCSG ▷ C3×C11×C41
UCSC1

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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×#17985247, D3×#17985241, D3×#17985235, …
maximal normal subgroup ofD3×#17985247, D3×#17985241, D3×#17985235, …
maximal quotient ofDic3×#14555919, C2×D3×#14555919

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13530, 43);