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C2×D5467 #36346142

order21868
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD10934
direct productC2×D5467
unambiguous semidirect product(C2×C7)⋊D781
unambiguous semidirect product(C2×C11)⋊D497
unambiguous semidirect product(C2×C71)⋊D77

Splittings

Fitting, socleC2×C7×C11×C71 ⋊ C2
derived, HallC7×C11×C71 ⋊ C22
HallC11×C71 ⋊ C2×D7
HallC7×C71 ⋊ C2×D11
HallC7×C11 ⋊ C2×D71
SylowC71 ⋊ C2×D77
SylowC11 ⋊ C2×D497
SylowC7 ⋊ C2×D781

Subgroups

subgroupG/H
center, hypercenterC2D5467
commutator, cosocle, hypocenterC7×C11×C71C22
FrattiniC1G
Fitting, socleC2×C7×C11×C71C2
LCSG ▷ C7×C11×C71
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 91
transitive degreeμt(G) = 10934

A minimal faithful permutation representation — 2 generators on 91 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);(4,9)(5,8)(6,7)(11,20)(12,19)(13,18)(14,17)(15,16)(22,91)(23,90)(24,89)(25,88)(26,87)(27,86)(28,85)(29,84)(30,83)(31,82)(32,81)(33,80)(34,79)(35,78)(36,77)(37,76)(38,75)(39,74)(40,73)(41,72)(42,71)(43,70)(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(56,57)

Conjugacy classes & character table

5470 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD21868
maximal normal subgroup ofD21868
maximal quotient ofDic10934, D21868

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21868, 32);