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C3×D3×C67⋊C11 #27210712

order13266
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3×C67⋊C11
unambiguous semidirect productC3⋊(C2×C3×C67⋊C11)
unambiguous semidirect product(C3×D3×C67)⋊C11

Splittings

Fitting, socle, HallC32×C67 ⋊ C2×C11
derivedC3×C67 ⋊ C2×C3×C11
HallC32×C67⋊C11 ⋊ C2
HallC3×D3×C67 ⋊ C11
SylowC67 ⋊ C3×D3×C11
SylowC32 ⋊ C2×C67⋊C11

Subgroups

subgroupG/H
center, hypercenterC3D3×C67⋊C11
commutator, cosocle, hypocenterC3×C67C2×C3×C11
FrattiniC1G
Fitting, socleC32×C67C2×C11
LCSG ▷ C3×C67
UCSC1 ◁ C3

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 402

A minimal faithful permutation representation — 2 generators on 73 points:

(2,3,5,9,17,31,28,46,14,25,43)(4,7,13,23,41,38,57,66,63,67,65)(6,11,21,37,53,61,44,24,10,19,33)(8,15,27,45,32,40,52,30,50,64,12)(16,29,48,51,49,62,55,59,58,47,60)(18,20,35,54,34,42,22,39,26,36,56)(68,69,70)(72,73);(1,2,4,8,16,30,11,22,40,5,10,20,36,23,17,25,44,61,13,24,42,60,43,33,46,31,51,27,41,59,67,56,54,62,35,55,48,19,34,53,9,18,32,52,65,64,39,58,66,21,38,57,50,45,37,29,49,63,15,28,47,7,14,26,3,6,12)(71,72,73)

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×D67⋊C11, D3×C3⋊(D67⋊C11), D32×C67⋊C11, …
maximal normal subgroup ofC3×D3×D67⋊C11, D3×C3⋊(D67⋊C11), D32×C67⋊C11, …
maximal quotient ofC3×Dic3×C67⋊C11, C2×C3×D3×C67⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 26);