Finite Group Databasebeta

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C2×D9265 #49150420

order37060
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD18530
direct productC2×D9265
unambiguous semidirect product(C2×C5)⋊D1853
unambiguous semidirect product(C2×C17)⋊D545
unambiguous semidirect product(C2×C109)⋊D85

Splittings

Fitting, socleC2×C5×C17×C109 ⋊ C2
derived, HallC5×C17×C109 ⋊ C22
HallC17×C109 ⋊ C2×D5
HallC5×C109 ⋊ C2×D17
SylowC109 ⋊ C2×D85
HallC5×C17 ⋊ C2×D109
SylowC17 ⋊ C2×D545
SylowC5 ⋊ C2×D1853

Subgroups

subgroupG/H
center, hypercenterC2D9265
commutator, cosocle, hypocenterC5×C17×C109C22
FrattiniC1G
Fitting, socleC2×C5×C17×C109C2
LCSG ▷ C5×C17×C109
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 133
transitive degreeμt(G) = 18530

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

Conjugacy classes & character table

9268 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37060, 51);