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C2×D4773 #34061898

order19092
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9546
direct productC2×D4773
unambiguous semidirect product(C2×C3)⋊D1591
unambiguous semidirect product(C2×C37)⋊D129
unambiguous semidirect product(C2×C43)⋊D111

Splittings

Fitting, socleC2×C3×C37×C43 ⋊ C2
derived, HallC3×C37×C43 ⋊ C22
HallC37×C43 ⋊ C2×D3
HallC3×C43 ⋊ C2×D37
HallC3×C37 ⋊ C2×D43
SylowC43 ⋊ C2×D111
SylowC37 ⋊ C2×D129
SylowC3 ⋊ C2×D1591

Subgroups

subgroupG/H
center, hypercenterC2D4773
commutator, cosocle, hypocenterC3×C37×C43C22
FrattiniC1G
Fitting, socleC2×C3×C37×C43C2
LCSG ▷ C3×C37×C43
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 85
transitive degreeμt(G) = 9546

A minimal faithful permutation representation — 2 generators on 85 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);(4,5)(7,42)(8,41)(9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(44,85)(45,84)(46,83)(47,82)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)

Conjugacy classes & character table

4776 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD19092, C2×D14319
maximal normal subgroup ofD19092
maximal quotient ofDic9546, D19092, C2×D14319

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19092, 70);