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C2×D8569 #46804662

order34276
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD17138
direct productC2×D8569
unambiguous semidirect product(C2×C11)⋊D779
unambiguous semidirect product(C2×C19)⋊D451
unambiguous semidirect product(C2×C41)⋊D209

Splittings

Fitting, socleC2×C11×C19×C41 ⋊ C2
derived, HallC11×C19×C41 ⋊ C22
HallC19×C41 ⋊ C2×D11
HallC11×C41 ⋊ C2×D19
HallC11×C19 ⋊ C2×D41
SylowC41 ⋊ C2×D209
SylowC19 ⋊ C2×D451
SylowC11 ⋊ C2×D779

Subgroups

subgroupG/H
center, hypercenterC2D8569
commutator, cosocle, hypocenterC11×C19×C41C22
FrattiniC1G
Fitting, socleC2×C11×C19×C41C2
LCSG ▷ C11×C19×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 17138

A minimal faithful permutation representation — 2 generators on 73 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(34,73)(35,72)(36,71)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,64)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58)(50,57)(51,56)(52,55)(53,54)

Conjugacy classes & character table

8572 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34276, 27);