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Cayley diagram

C2×D87 #66832

order348
isoclinismisoclinic class of D87
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD174
direct productC2×D87
unambiguous semidirect product(C2×C3)⋊D29
unambiguous semidirect product(C2×C29)⋊D3

Splittings

Fitting, socleC2×C3×C29 ⋊ C2
derived, HallC3×C29 ⋊ C22
SylowC29 ⋊ C2×D3
SylowC3 ⋊ C2×D29

Subgroups

subgroupG/H
center, hypercenterC2D87
commutator, cosocle, hypocenterC3×C29C22
FrattiniC1G
Fitting, socleC2×C3×C29C2
LCSG ▷ C3×C29
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 174

A minimal faithful permutation representation — 2 generators on 34 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);(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)

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10621942, #10621944, #10621945, …
maximal normal subgroup of#10621942, #10621944, #10621945, …
maximal quotient ofDic174, C4×D87, D348, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(348, 11);