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C2×D5335 #36319385

order21340
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD10670
direct productC2×D5335
unambiguous semidirect product(C2×C5)⋊D1067
unambiguous semidirect product(C2×C11)⋊D485
unambiguous semidirect product(C2×C97)⋊D55

Splittings

Fitting, socleC2×C5×C11×C97 ⋊ C2
derived, HallC5×C11×C97 ⋊ C22
HallC11×C97 ⋊ C2×D5
HallC5×C97 ⋊ C2×D11
SylowC97 ⋊ C2×D55
HallC5×C11 ⋊ C2×D97
SylowC11 ⋊ C2×D485
SylowC5 ⋊ C2×D1067

Subgroups

subgroupG/H
center, hypercenterC2D5335
commutator, cosocle, hypocenterC5×C11×C97C22
FrattiniC1G
Fitting, socleC2×C5×C11×C97C2
LCSG ▷ C5×C11×C97
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 115
transitive degreeμt(G) = 10670

A minimal faithful permutation representation — 2 generators on 115 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(4,7)(5,6)(9,18)(10,17)(11,16)(12,15)(13,14)(20,115)(21,114)(22,113)(23,112)(24,111)(25,110)(26,109)(27,108)(28,107)(29,106)(30,105)(31,104)(32,103)(33,102)(34,101)(35,100)(36,99)(37,98)(38,97)(39,96)(40,95)(41,94)(42,93)(43,92)(44,91)(45,90)(46,89)(47,88)(48,87)(49,86)(50,85)(51,84)(52,83)(53,82)(54,81)(55,80)(56,79)(57,78)(58,77)(59,76)(60,75)(61,74)(62,73)(63,72)(64,71)(65,70)(66,69)(67,68)

Conjugacy classes & character table

5338 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD21340, C2×D16005
maximal normal subgroup ofD21340
maximal quotient ofDic10670, D21340, C2×D16005

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21340, 46);