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C2×D8525 #46801984

order34100
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD17050
direct productC2×D8525
unambiguous semidirect product(C2×C11)⋊D775
unambiguous semidirect product(C2×C25)⋊D341
unambiguous semidirect product(C2×C31)⋊D275

Splittings

FittingC2×C11×C25×C31 ⋊ C2
derived, HallC11×C25×C31 ⋊ C22
HallC25×C31 ⋊ C2×D11
HallC11×C31 ⋊ C2×D25
HallC11×C25 ⋊ C2×D31
SylowC31 ⋊ C2×D275
SylowC25 ⋊ C2×D341
SylowC11 ⋊ C2×D775

Subgroups

subgroupG/H
center, hypercenterC2D8525
commutator, cosocle, hypocenterC11×C25×C31C22
FrattiniC5C2×D1705
FittingC2×C11×C25×C31C2
socleC2×C5×C11×C31D5
LCSG ▷ C11×C25×C31
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 69
transitive degreeμt(G) = 17050

A minimal faithful permutation representation — 2 generators on 69 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);(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(29,38)(30,37)(31,36)(32,35)(33,34)(40,69)(41,68)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)

Conjugacy classes & character table

8528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 75);