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C2×D3905 #30626842

order15620
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD7810
direct productC2×D3905
unambiguous semidirect product(C2×C5)⋊D781
unambiguous semidirect product(C2×C11)⋊D355
unambiguous semidirect product(C2×C71)⋊D55

Splittings

Fitting, socleC2×C5×C11×C71 ⋊ C2
derived, HallC5×C11×C71 ⋊ C22
HallC11×C71 ⋊ C2×D5
HallC5×C71 ⋊ C2×D11
SylowC71 ⋊ C2×D55
HallC5×C11 ⋊ C2×D71
SylowC11 ⋊ C2×D355
SylowC5 ⋊ C2×D781

Subgroups

subgroupG/H
center, hypercenterC2D3905
commutator, cosocle, hypocenterC5×C11×C71C22
FrattiniC1G
Fitting, socleC2×C5×C11×C71C2
LCSG ▷ C5×C11×C71
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 89
transitive degreeμt(G) = 7810

A minimal faithful permutation representation — 2 generators on 89 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);(4,7)(5,6)(9,18)(10,17)(11,16)(12,15)(13,14)(20,89)(21,88)(22,87)(23,86)(24,85)(25,84)(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

3908 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD15620
maximal normal subgroup ofD15620
maximal quotient ofDic7810, D15620

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15620, 75);