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Cayley diagram

C2×D69 #63287

order276
isoclinismisoclinic class of D69
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD138
direct productC2×D69
unambiguous semidirect product(C2×C3)⋊D23
unambiguous semidirect product(C2×C23)⋊D3

Splittings

Fitting, socleC2×C3×C23 ⋊ C2
derived, HallC3×C23 ⋊ C22
SylowC23 ⋊ C2×D3
SylowC3 ⋊ C2×D23

Subgroups

subgroupG/H
center, hypercenterC2D69
commutator, cosocle, hypocenterC3×C23C22
FrattiniC1G
Fitting, socleC2×C3×C23C2
LCSG ▷ C3×C23
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 138

A minimal faithful permutation representation — 2 generators on 28 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);(4,5)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD69⋊C4, #10587771, #10587772, …
maximal normal subgroup ofD69⋊C4, #10587771, #10587772, …
maximal quotient ofDic138, C4×D69, D276, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(276, 9);