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C2×D5719 #37504244

order22876
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11438
direct productC2×D5719
unambiguous semidirect product(C2×C7)⋊D817
unambiguous semidirect product(C2×C19)⋊D301
unambiguous semidirect product(C2×C43)⋊D133

Splittings

Fitting, socleC2×C7×C19×C43 ⋊ C2
derived, HallC7×C19×C43 ⋊ C22
HallC19×C43 ⋊ C2×D7
HallC7×C43 ⋊ C2×D19
HallC7×C19 ⋊ C2×D43
SylowC43 ⋊ C2×D133
SylowC19 ⋊ C2×D301
SylowC7 ⋊ C2×D817

Subgroups

subgroupG/H
center, hypercenterC2D5719
commutator, cosocle, hypocenterC7×C19×C43C22
FrattiniC1G
Fitting, socleC2×C7×C19×C43C2
LCSG ▷ C7×C19×C43
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 71
transitive degreeμt(G) = 11438

A minimal faithful permutation representation — 2 generators on 71 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);(4,9)(5,8)(6,7)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(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

5722 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD22876
maximal normal subgroup ofD22876
maximal quotient ofDic11438, D22876

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22876, 32);