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C2×D4895 #34086623

order19580
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9790
direct productC2×D4895
unambiguous semidirect product(C2×C5)⋊D979
unambiguous semidirect product(C2×C11)⋊D445
unambiguous semidirect product(C2×C89)⋊D55

Splittings

Fitting, socleC2×C5×C11×C89 ⋊ C2
derived, HallC5×C11×C89 ⋊ C22
HallC11×C89 ⋊ C2×D5
HallC5×C89 ⋊ C2×D11
SylowC89 ⋊ C2×D55
HallC5×C11 ⋊ C2×D89
SylowC11 ⋊ C2×D445
SylowC5 ⋊ C2×D979

Subgroups

subgroupG/H
center, hypercenterC2D4895
commutator, cosocle, hypocenterC5×C11×C89C22
FrattiniC1G
Fitting, socleC2×C5×C11×C89C2
LCSG ▷ C5×C11×C89
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 107
transitive degreeμt(G) = 9790

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

Conjugacy classes & character table

4898 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD19580, C2×D14685
maximal normal subgroup ofD19580
maximal quotient ofDic9790, D19580, C2×D14685

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19580, 55);