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Cayley diagram

C3×D53 #64659

order318
isoclinismisoclinic class of D53
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D53
unambiguous semidirect productC53⋊(C2×C3)

Splittings

Fitting, socle, HallC3×C53 ⋊ C2
derived, SylowC53 ⋊ C2×C3

Subgroups

subgroupG/H
center, hypercenterC3D53
commutator, cosocle, hypocenterC53C2×C3
FrattiniC1G
Fitting, socleC3×C53C2
LCSG ▷ C53
UCSC1 ◁ C3

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 159

A minimal faithful permutation representation — 2 generators on 56 points:

(1,2,3)(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);(4,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#6157, C3⋊#6157, D3×D53, …
maximal normal subgroup ofC3×#6157, C3⋊#6157, D3×D53, …
maximal quotient ofC3×Dic53, C2×C3×D53, C9×D53, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(318, 2);