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C2×D3965 #30629466

order15860
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD7930
direct productC2×D3965
unambiguous semidirect product(C2×C5)⋊D793
unambiguous semidirect product(C2×C13)⋊D305
unambiguous semidirect product(C2×C61)⋊D65

Splittings

Fitting, socleC2×C5×C13×C61 ⋊ C2
derived, HallC5×C13×C61 ⋊ C22
HallC13×C61 ⋊ C2×D5
HallC5×C61 ⋊ C2×D13
HallC5×C13 ⋊ C2×D61
SylowC61 ⋊ C2×D65
SylowC13 ⋊ C2×D305
SylowC5 ⋊ C2×D793

Subgroups

subgroupG/H
center, hypercenterC2D3965
commutator, cosocle, hypocenterC5×C13×C61C22
FrattiniC1G
Fitting, socleC2×C5×C13×C61C2
LCSG ▷ C5×C13×C61
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 81
transitive degreeμt(G) = 7930

A minimal faithful permutation representation — 2 generators on 81 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);(4,7)(5,6)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(22,81)(23,80)(24,79)(25,78)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Conjugacy classes & character table

3968 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD15860
maximal normal subgroup ofD15860
maximal quotient ofDic7930, D15860

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15860, 60);