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C2×D6721 #41001892

order26884
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD13442
direct productC2×D6721
unambiguous semidirect product(C2×C11)⋊D611
unambiguous semidirect product(C2×C13)⋊D517
unambiguous semidirect product(C2×C47)⋊D143

Splittings

Fitting, socleC2×C11×C13×C47 ⋊ C2
derived, HallC11×C13×C47 ⋊ C22
HallC13×C47 ⋊ C2×D11
HallC11×C47 ⋊ C2×D13
HallC11×C13 ⋊ C2×D47
SylowC47 ⋊ C2×D143
SylowC13 ⋊ C2×D517
SylowC11 ⋊ C2×D611

Subgroups

subgroupG/H
center, hypercenterC2D6721
commutator, cosocle, hypocenterC11×C13×C47C22
FrattiniC1G
Fitting, socleC2×C11×C13×C47C2
LCSG ▷ C11×C13×C47
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 13442

A minimal faithful permutation representation — 2 generators on 73 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(28,73)(29,72)(30,71)(31,70)(32,69)(33,68)(34,67)(35,66)(36,65)(37,64)(38,63)(39,62)(40,61)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)

Conjugacy classes & character table

6724 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD26884
maximal normal subgroup ofD26884
maximal quotient ofDic13442, D26884

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26884, 27);