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C2×D5355 #36339282

order21420
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD10710
direct productC2×D5355
unambiguous semidirect product(C2×C5)⋊D1071
unambiguous semidirect product(C2×C7)⋊D765
unambiguous semidirect product(C2×C9)⋊D595
unambiguous semidirect product(C2×C17)⋊D315

Splittings

FittingC2×C5×C7×C9×C17 ⋊ C2
derived, HallC5×C7×C9×C17 ⋊ C22
HallC7×C9×C17 ⋊ C2×D5
HallC5×C9×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D17
HallC9×C17 ⋊ C2×D35
HallC7×C17 ⋊ C2×D45
HallC5×C17 ⋊ C2×D63
HallC7×C9 ⋊ C2×D85
HallC5×C9 ⋊ C2×D119
HallC5×C7 ⋊ C2×D153
SylowC17 ⋊ C2×D315
SylowC9 ⋊ C2×D595
SylowC7 ⋊ C2×D765
SylowC5 ⋊ C2×D1071

Subgroups

subgroupG/H
center, hypercenterC2D5355
commutator, cosocle, hypocenterC5×C7×C9×C17C22
FrattiniC3C2×D1785
FittingC2×C5×C7×C9×C17C2
socleC2×C3×C5×C7×C17D3
LCSG ▷ C5×C7×C9×C17
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 10710

A minimal faithful permutation representation — 2 generators on 40 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);(4,11)(5,10)(6,9)(7,8)(13,16)(14,15)(18,23)(19,22)(20,21)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)

Conjugacy classes & character table

5358 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD21420, C2×D16065
maximal normal subgroup ofD21420
maximal quotient ofDic10710, D21420, C2×D16065

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 114);