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C2×D5829 #37552198

order23316
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11658
direct productC2×D5829
unambiguous semidirect product(C2×C3)⋊D1943
unambiguous semidirect product(C2×C29)⋊D201
unambiguous semidirect product(C2×C67)⋊D87

Splittings

Fitting, socleC2×C3×C29×C67 ⋊ C2
derived, HallC3×C29×C67 ⋊ C22
HallC29×C67 ⋊ C2×D3
HallC3×C67 ⋊ C2×D29
HallC3×C29 ⋊ C2×D67
SylowC67 ⋊ C2×D87
SylowC29 ⋊ C2×D201
SylowC3 ⋊ C2×D1943

Subgroups

subgroupG/H
center, hypercenterC2D5829
commutator, cosocle, hypocenterC3×C29×C67C22
FrattiniC1G
Fitting, socleC2×C3×C29×C67C2
LCSG ▷ C3×C29×C67
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 101
transitive degreeμt(G) = 11658

A minimal faithful permutation representation — 2 generators on 101 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)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(4,5)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(36,101)(37,100)(38,99)(39,98)(40,97)(41,96)(42,95)(43,94)(44,93)(45,92)(46,91)(47,90)(48,89)(49,88)(50,87)(51,86)(52,85)(53,84)(54,83)(55,82)(56,81)(57,80)(58,79)(59,78)(60,77)(61,76)(62,75)(63,74)(64,73)(65,72)(66,71)(67,70)(68,69)

Conjugacy classes & character table

5832 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23316
maximal normal subgroup ofD23316
maximal quotient ofDic11658, D23316

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23316, 40);