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C2×D9447 #49180238

order37788
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD18894
direct productC2×D9447
unambiguous semidirect product(C2×C3)⋊D3149
unambiguous semidirect product(C2×C47)⋊D201
unambiguous semidirect product(C2×C67)⋊D141

Splittings

Fitting, socleC2×C3×C47×C67 ⋊ C2
derived, HallC3×C47×C67 ⋊ C22
HallC47×C67 ⋊ C2×D3
HallC3×C67 ⋊ C2×D47
HallC3×C47 ⋊ C2×D67
SylowC67 ⋊ C2×D141
SylowC47 ⋊ C2×D201
SylowC3 ⋊ C2×D3149

Subgroups

subgroupG/H
center, hypercenterC2D9447
commutator, cosocle, hypocenterC3×C47×C67C22
FrattiniC1G
Fitting, socleC2×C3×C47×C67C2
LCSG ▷ C3×C47×C67
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 119
transitive degreeμt(G) = 18894

A minimal faithful permutation representation — 2 generators on 119 points:

(1,2)(3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)(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);(4,5)(7,52)(8,51)(9,50)(10,49)(11,48)(12,47)(13,46)(14,45)(15,44)(16,43)(17,42)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(54,119)(55,118)(56,117)(57,116)(58,115)(59,114)(60,113)(61,112)(62,111)(63,110)(64,109)(65,108)(66,107)(67,106)(68,105)(69,104)(70,103)(71,102)(72,101)(73,100)(74,99)(75,98)(76,97)(77,96)(78,95)(79,94)(80,93)(81,92)(82,91)(83,90)(84,89)(85,88)(86,87)

Conjugacy classes & character table

9450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37788, 34);