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D3×C11×C29⋊C7 #27211531

order13398
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productD3×C11×C29⋊C7
unambiguous semidirect productC3⋊(C2×C11×C29⋊C7)
unambiguous semidirect product(D3×C29)⋊(C7×C11)
unambiguous semidirect product(D3×C11×C29)⋊C7

Splittings

Fitting, socle, HallC3×C11×C29 ⋊ C2×C7
derived, HallC3×C29 ⋊ C2×C7×C11
HallC3×C11×C29⋊C7 ⋊ C2
HallD3×C11×C29 ⋊ C7
HallC3×C29⋊C7 ⋊ C2×C11
HallC11×C29 ⋊ D3×C7
HallD3×C29 ⋊ C7×C11
HallC3×C11 ⋊ C2×C29⋊C7
SylowC29 ⋊ D3×C7×C11
SylowC3 ⋊ C2×C11×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC11D3×C29⋊C7
commutator, cosocle, hypocenterC3×C29C2×C7×C11
FrattiniC1G
Fitting, socleC3×C11×C29C2×C7
LCSG ▷ C3×C29
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 957

A minimal faithful permutation representation — 2 generators on 43 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×C11×D29⋊C7, D3×C11⋊(D29⋊C7), D3×D11×C29⋊C7, …
maximal normal subgroup ofD3×C11×D29⋊C7, D3×C11⋊(D29⋊C7), D3×D11×C29⋊C7, …
maximal quotient ofC11×Dic3×C29⋊C7, C2×D3×C11×C29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 22);