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C2×D5015 #34095425

order20060
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD10030
direct productC2×D5015
unambiguous semidirect product(C2×C5)⋊D1003
unambiguous semidirect product(C2×C17)⋊D295
unambiguous semidirect product(C2×C59)⋊D85

Splittings

Fitting, socleC2×C5×C17×C59 ⋊ C2
derived, HallC5×C17×C59 ⋊ C22
HallC17×C59 ⋊ C2×D5
HallC5×C59 ⋊ C2×D17
HallC5×C17 ⋊ C2×D59
SylowC59 ⋊ C2×D85
SylowC17 ⋊ C2×D295
SylowC5 ⋊ C2×D1003

Subgroups

subgroupG/H
center, hypercenterC2D5015
commutator, cosocle, hypocenterC5×C17×C59C22
FrattiniC1G
Fitting, socleC2×C5×C17×C59C2
LCSG ▷ C5×C17×C59
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 83
transitive degreeμt(G) = 10030

A minimal faithful permutation representation — 2 generators on 83 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);(4,7)(5,6)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(26,83)(27,82)(28,81)(29,80)(30,79)(31,78)(32,77)(33,76)(34,75)(35,74)(36,73)(37,72)(38,71)(39,70)(40,69)(41,68)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)

Conjugacy classes & character table

5018 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD20060, C2×D15045
maximal normal subgroup ofD20060
maximal quotient ofDic10030, D20060, C2×D15045

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20060, 35);