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C2×D4899 #34086687

order19596
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9798
direct productC2×D4899
unambiguous semidirect product(C2×C3)⋊D1633
unambiguous semidirect product(C2×C23)⋊D213
unambiguous semidirect product(C2×C71)⋊D69

Splittings

Fitting, socleC2×C3×C23×C71 ⋊ C2
derived, HallC3×C23×C71 ⋊ C22
HallC23×C71 ⋊ C2×D3
HallC3×C71 ⋊ C2×D23
SylowC71 ⋊ C2×D69
HallC3×C23 ⋊ C2×D71
SylowC23 ⋊ C2×D213
SylowC3 ⋊ C2×D1633

Subgroups

subgroupG/H
center, hypercenterC2D4899
commutator, cosocle, hypocenterC3×C23×C71C22
FrattiniC1G
Fitting, socleC2×C3×C23×C71C2
LCSG ▷ C3×C23×C71
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 99
transitive degreeμt(G) = 9798

A minimal faithful permutation representation — 2 generators on 99 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);(4,5)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(30,99)(31,98)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,90)(40,89)(41,88)(42,87)(43,86)(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

4902 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD19596, C2×D14697
maximal normal subgroup ofD19596
maximal quotient ofDic9798, D19596, C2×D14697

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19596, 18);