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Cayley diagram

C3⋊#4179 #92328

order486
isoclinismisoclinic class of C3⋊#4179
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C32

Aliases

unambiguous semidirect productC3⋊#4179

Splittings

Fitting, SylowC3×#732 ⋊ C2
derivedC32×C9 ⋊ C2×C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC32×C9C2×C3
FrattiniC32C3×C3⋊D3
FittingC3×#732C2
socleC32(C3⋊D3)⋊C3
LCSG ▷ C32×C9
UCSC1

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 81

A minimal faithful permutation representation — 3 generators on 30 points:

(2,3)(5,15,18,8,9,19)(6,24,26,12,13,25)(7,14)(10,21,28,11,22,29)(16,23,27,20,17,30);(1,2,3);(4,23,8,14,11,10,7,5,17)(6,30,16,26,21,19,13,9,28)(12,29,15,24,18,22,25,20,27)

Polycyclic presentation:

2,3^5|c^3=f^2,c^a=c^2f,d^a=d^2,e^a=e^2,f^a=f^2,c^b=ce,e^b=ef

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#4179, #11757741, #11757757, …
maximal normal subgroup ofD3×#4179, #11757741, #11757757, …
maximal quotient ofC3⋊#66326, C2×C3⋊#4179, C3⋊#92160, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 173);