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C2×D4929 #34089333

order19716
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9858
direct productC2×D4929
unambiguous semidirect product(C2×C3)⋊D1643
unambiguous semidirect product(C2×C31)⋊D159
unambiguous semidirect product(C2×C53)⋊D93

Splittings

Fitting, socleC2×C3×C31×C53 ⋊ C2
derived, HallC3×C31×C53 ⋊ C22
HallC31×C53 ⋊ C2×D3
HallC3×C53 ⋊ C2×D31
HallC3×C31 ⋊ C2×D53
SylowC53 ⋊ C2×D93
SylowC31 ⋊ C2×D159
SylowC3 ⋊ C2×D1643

Subgroups

subgroupG/H
center, hypercenterC2D4929
commutator, cosocle, hypocenterC3×C31×C53C22
FrattiniC1G
Fitting, socleC2×C3×C31×C53C2
LCSG ▷ C3×C31×C53
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 89
transitive degreeμt(G) = 9858

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

Conjugacy classes & character table

4932 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD19716, C2×D14787
maximal normal subgroup ofD19716
maximal quotient ofDic9858, D19716, C2×D14787

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19716, 34);