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C2×D4355 #31775191

order17420
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD8710
direct productC2×D4355
unambiguous semidirect product(C2×C5)⋊D871
unambiguous semidirect product(C2×C13)⋊D335
unambiguous semidirect product(C2×C67)⋊D65

Splittings

Fitting, socleC2×C5×C13×C67 ⋊ C2
derived, HallC5×C13×C67 ⋊ C22
HallC13×C67 ⋊ C2×D5
HallC5×C67 ⋊ C2×D13
SylowC67 ⋊ C2×D65
HallC5×C13 ⋊ C2×D67
SylowC13 ⋊ C2×D335
SylowC5 ⋊ C2×D871

Subgroups

subgroupG/H
center, hypercenterC2D4355
commutator, cosocle, hypocenterC5×C13×C67C22
FrattiniC1G
Fitting, socleC2×C5×C13×C67C2
LCSG ▷ C5×C13×C67
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 87
transitive degreeμt(G) = 8710

A minimal faithful permutation representation — 2 generators on 87 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);(4,7)(5,6)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(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

4358 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD17420, C2×D13065
maximal normal subgroup ofD17420
maximal quotient ofDic8710, D17420, C2×D13065

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17420, 29);