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C2×C11×C31⋊C3 #14523296

order2046
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×C31⋊C3
unambiguous semidirect product(C2×C31)⋊(C3×C11)
unambiguous semidirect product(C2×C11×C31)⋊C3

Splittings

Fitting, socle, HallC2×C11×C31 ⋊ C3
derived, SylowC31 ⋊ C2×C3×C11
HallC11×C31 ⋊ C2×C3
HallC2×C31 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11C31⋊C3
commutator, cosocle, hypocenterC31C2×C3×C11
FrattiniC1G
Fitting, socleC2×C11×C31C3
LCSG ▷ C31
UCSC1 ◁ C2×C11

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 682

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC4×C11×C31⋊C3, C11×(C31⋊C3)⋊C4, Dic11×C31⋊C3, …
maximal normal subgroup ofC4×C11×C31⋊C3, C11×(C31⋊C3)⋊C4, Dic11×C31⋊C3, …
maximal quotient ofC4×C11×C31⋊C3, C22×C11×C31⋊C3, C2×C7×C11×C31⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2046, 2);