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C2×D5883 #37555244

order23532
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11766
direct productC2×D5883
unambiguous semidirect product(C2×C3)⋊D1961
unambiguous semidirect product(C2×C37)⋊D159
unambiguous semidirect product(C2×C53)⋊D111

Splittings

Fitting, socleC2×C3×C37×C53 ⋊ C2
derived, HallC3×C37×C53 ⋊ C22
HallC37×C53 ⋊ C2×D3
HallC3×C53 ⋊ C2×D37
HallC3×C37 ⋊ C2×D53
SylowC53 ⋊ C2×D111
SylowC37 ⋊ C2×D159
SylowC3 ⋊ C2×D1961

Subgroups

subgroupG/H
center, hypercenterC2D5883
commutator, cosocle, hypocenterC3×C37×C53C22
FrattiniC1G
Fitting, socleC2×C3×C37×C53C2
LCSG ▷ C3×C37×C53
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 95
transitive degreeμt(G) = 11766

A minimal faithful permutation representation — 2 generators on 95 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);(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)(44,95)(45,94)(46,93)(47,92)(48,91)(49,90)(50,89)(51,88)(52,87)(53,86)(54,85)(55,84)(56,83)(57,82)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71)(69,70)

Conjugacy classes & character table

5886 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23532
maximal normal subgroup ofD23532
maximal quotient ofDic11766, D23532

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23532, 52);