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C2×C7×C3⋊D411 #46828684

order34524
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C7×C3⋊D411
unambiguous semidirect product(C2×C3)⋊(C7×D411)
unambiguous semidirect product(C2×C137)⋊(C7×C3⋊D3)

Splittings

Fitting, socleC2×C32×C7×C137 ⋊ C2
derived, HallC32×C137 ⋊ C22×C7
HallC32×C7×C137 ⋊ C22
HallC7×C137 ⋊ C2×C3⋊D3
SylowC137 ⋊ C2×C7×C3⋊D3
HallC32×C7 ⋊ C2×D137
SylowC32 ⋊ C2×C7×D137

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊D411
commutator, cosocle, hypocenterC32×C137C22×C7
FrattiniC1G
Fitting, socleC2×C32×C7×C137C2
LCSG ▷ C32×C137
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 152
transitive degreeμt(G) = 17262

A minimal faithful permutation representation — 3 generators on 152 points:

(4,5)(7,8)(9,10,11,12,13,14,15)(17,18)(19,20)(21,22)(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)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96)(97,98)(99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152);(1,2)(6,7,8)(16,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133,135,137,139,141,143,145,147,149,151,152,150,148,146,144,142,140,138,136,134,132,130,128,126,124,122,120,118,116,114,112,110,108,106,104,102,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18);(3,4,5)

Conjugacy classes & character table

8652 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34524, 127);