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D3×C7×D407 #46803267

order34188
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×D407
unambiguous semidirect product(D3×C11)⋊(C7×D37)
unambiguous semidirect product(D3×C37)⋊(C7×D11)

Splittings

Fitting, socle, HallC3×C7×C11×C37 ⋊ C22
derived, HallC3×C11×C37 ⋊ C22×C7
HallC7×C11×C37 ⋊ C2×D3
HallC3×C7×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×D3×C7
HallC7×C37 ⋊ D3×D11
HallC3×C7×C11 ⋊ C2×D37
HallC3×C37 ⋊ C2×C7×D11
HallC7×C11 ⋊ D3×D37
SylowC37 ⋊ D3×C7×D11
HallC3×C11 ⋊ C2×C7×D37
HallC3×C7 ⋊ C2×D407
SylowC11 ⋊ D3×C7×D37
SylowC3 ⋊ C2×C7×D407

Subgroups

subgroupG/H
center, hypercenterC7D3×D407
commutator, cosocle, hypocenterC3×C11×C37C22×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C37C22
LCSG ▷ C3×C11×C37
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 58
transitive degreeμt(G) = 8547

A minimal faithful permutation representation — 2 generators on 58 points:

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

Conjugacy classes & character table

4305 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 139);