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D11×C31⋊C3 #14523305

order2046
isoclinismisoclinic class of D11×C31⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productD11×C31⋊C3
unambiguous semidirect productC11⋊(C2×C31⋊C3)
unambiguous semidirect product(D11×C31)⋊C3

Splittings

Fitting, socle, derived, HallC11×C31 ⋊ C2×C3
HallC11×C31⋊C3 ⋊ C2
HallD11×C31 ⋊ C3
SylowC31 ⋊ C3×D11
SylowC11 ⋊ C2×C31⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C31C2×C3
LCSG ▷ C11×C31
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 341

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14,16)(15,18,23)(17,21,20)(19,25,32)(22,28,30)(24,26,27)(29,35,39)(31,36,37)(33,40,34)(38,41,42);(2,11)(3,10)(4,9)(5,8)(6,7)(12,13,15,19,26,16,20,27,34,40,23,30,37,25,33,32,39,42,35,18,24,31,38,41,28,14,17,22,29,36,21)

Conjugacy classes & character table

91 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×D31⋊C3, C2×D11×C31⋊C3, C7×D11×C31⋊C3, …
maximal normal subgroup ofD11×D31⋊C3, C2×D11×C31⋊C3, C7×D11×C31⋊C3, …
maximal quotient ofDic11×C31⋊C3, C2×D11×C31⋊C3, C7×D11×C31⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2046, 11);