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C2×D5781 #37528872

order23124
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11562
direct productC2×D5781
unambiguous semidirect product(C2×C3)⋊D1927
unambiguous semidirect product(C2×C41)⋊D141
unambiguous semidirect product(C2×C47)⋊D123

Splittings

Fitting, socleC2×C3×C41×C47 ⋊ C2
derived, HallC3×C41×C47 ⋊ C22
HallC41×C47 ⋊ C2×D3
HallC3×C47 ⋊ C2×D41
HallC3×C41 ⋊ C2×D47
SylowC47 ⋊ C2×D123
SylowC41 ⋊ C2×D141
SylowC3 ⋊ C2×D1927

Subgroups

subgroupG/H
center, hypercenterC2D5781
commutator, cosocle, hypocenterC3×C41×C47C22
FrattiniC1G
Fitting, socleC2×C3×C41×C47C2
LCSG ▷ C3×C41×C47
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 93
transitive degreeμt(G) = 11562

A minimal faithful permutation representation — 2 generators on 93 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);(4,5)(7,46)(8,45)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)

Conjugacy classes & character table

5784 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23124
maximal normal subgroup ofD23124
maximal quotient ofDic11562, D23124

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23124, 28);