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C2×D6665 #40998642

order26660
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD13330
direct productC2×D6665
unambiguous semidirect product(C2×C5)⋊D1333
unambiguous semidirect product(C2×C31)⋊D215
unambiguous semidirect product(C2×C43)⋊D155

Splittings

Fitting, socleC2×C5×C31×C43 ⋊ C2
derived, HallC5×C31×C43 ⋊ C22
HallC31×C43 ⋊ C2×D5
HallC5×C43 ⋊ C2×D31
HallC5×C31 ⋊ C2×D43
SylowC43 ⋊ C2×D155
SylowC31 ⋊ C2×D215
SylowC5 ⋊ C2×D1333

Subgroups

subgroupG/H
center, hypercenterC2D6665
commutator, cosocle, hypocenterC5×C31×C43C22
FrattiniC1G
Fitting, socleC2×C5×C31×C43C2
LCSG ▷ C5×C31×C43
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 81
transitive degreeμt(G) = 13330

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)(9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(40,81)(41,80)(42,79)(43,78)(44,77)(45,76)(46,75)(47,74)(48,73)(49,72)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)

Conjugacy classes & character table

6668 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD26660
maximal normal subgroup ofD26660
maximal quotient ofDic13330, D26660

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26660, 36);