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C3×C11⋊(D29⋊C7) #27211530

order13398
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊(D29⋊C7)
unambiguous semidirect productC11⋊(C3×D29⋊C7)
unambiguous semidirect product(C29⋊C7)⋊(C3×D11)
unambiguous semidirect productD319⋊(C3×C7)
unambiguous semidirect product(C3×D319)⋊C7

Splittings

Fitting, socle, HallC3×C11×C29 ⋊ C2×C7
derived, HallC11×C29 ⋊ C2×C3×C7
HallC3×C11×C29⋊C7 ⋊ C2
HallC11×C29⋊C7 ⋊ C2×C3
HallC3×D319 ⋊ C7
HallD319 ⋊ C3×C7
HallC3×C29⋊C7 ⋊ D11
HallC29⋊C7 ⋊ C3×D11
HallC3×C29 ⋊ C7×D11
HallC3×C11 ⋊ D29⋊C7
SylowC29 ⋊ C3×C7×D11
SylowC11 ⋊ C3×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC3C11⋊(D29⋊C7)
commutator, cosocle, hypocenterC11×C29C2×C3×C7
FrattiniC1G
Fitting, socleC3×C11×C29C2×C7
LCSG ▷ C11×C29
UCSC1 ◁ C3

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:

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

Conjugacy classes & character table

213 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D11×D29⋊C7, D3×C11⋊(D29⋊C7), D33⋊(D29⋊C7), …
maximal normal subgroup ofC3×D11×D29⋊C7, D3×C11⋊(D29⋊C7), D33⋊(D29⋊C7), …
maximal quotient ofC3×C11⋊(Dic29⋊C7), C2×C3×C11⋊(D29⋊C7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 21);