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C11×C3⋊(D29⋊C7) #27211532

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

Aliases

direct productC11×C3⋊(D29⋊C7)
unambiguous semidirect productC3⋊(C11×D29⋊C7)
unambiguous semidirect productD87⋊(C7×C11)
unambiguous semidirect product(C29⋊C7)⋊(D3×C11)
unambiguous semidirect product(C11×D87)⋊C7

Splittings

Fitting, socle, HallC3×C11×C29 ⋊ C2×C7
derived, HallC3×C29 ⋊ C2×C7×C11
HallC3×C11×C29⋊C7 ⋊ C2
HallC11×C29⋊C7 ⋊ D3
HallC11×D87 ⋊ C7
HallC3×C29⋊C7 ⋊ C2×C11
HallC11×C29 ⋊ D3×C7
HallC29⋊C7 ⋊ D3×C11
HallD87 ⋊ C7×C11
HallC3×C11 ⋊ D29⋊C7
SylowC29 ⋊ D3×C7×C11
SylowC3 ⋊ C11×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(D29⋊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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×C11×D29⋊C7, D11×C3⋊(D29⋊C7), D33⋊(D29⋊C7), …
maximal normal subgroup ofD3×C11×D29⋊C7, D11×C3⋊(D29⋊C7), D33⋊(D29⋊C7), …
maximal quotient ofC11×C3⋊(Dic29⋊C7), C2×C11×C3⋊(D29⋊C7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 23);