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D3×C7×C11×C29 #27211520

order13398
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C2×C7×C11×C29 · Schur multiplier (H2) = C1

Aliases

direct productD3×C7×C11×C29
unambiguous semidirect productC3⋊(C2×C7×C11×C29)

Splittings

Fitting, socle, HallC3×C7×C11×C29 ⋊ C2
derived, SylowC3 ⋊ C2×C7×C11×C29
HallC3×C11×C29 ⋊ C2×C7
HallC3×C7×C29 ⋊ C2×C11
HallC3×C7×C11 ⋊ C2×C29
HallC3×C29 ⋊ C2×C7×C11
HallC3×C11 ⋊ C2×C7×C29
HallC3×C7 ⋊ C2×C11×C29

Subgroups

subgroupG/H
center, hypercenterC7×C11×C29D3
commutator, cosocle, hypocenterC3C2×C7×C11×C29
FrattiniC1G
Fitting, socleC3×C7×C11×C29C2
LCSG ▷ C3
UCSC1 ◁ C7×C11×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 6699

A minimal faithful permutation representation — 2 generators on 50 points:

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

Conjugacy classes & character table

6699 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C7×C11×D29, D3×C7×D11×C29, D3×C7×D319, …
maximal normal subgroup ofD3×C7×C11×D29, D3×C7×D11×C29, D3×C7×D319, …
maximal quotient ofC7×C11×Dic3×C29, C2×D3×C7×C11×C29

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 11);