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Cayley diagram

#4207⋊C3 #92393

order486
isoclinismisoclinic class of #4207⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C32

Aliases

unambiguous semidirect product#4207⋊C3

Splittings

Fitting, Sylow3−1+4 ⋊ C2
derivedC3×C9 ⋊ C2×C32

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×C9C2×C32
Frattini, socleC3C32×C3⋊D3
Fitting3−1+4C2
LCSG ▷ C3×C9
UCSC1

181 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 27

A minimal faithful permutation representation — 3 generators on 27 points:

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

Polycyclic presentation:

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

Conjugacy classes & character table

55 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#4207⋊C2)⋊C3, C2×#4207⋊C3, (#4169⋊C3)⋊C3, …
maximal normal subgroup of(#4207⋊C2)⋊C3, C2×#4207⋊C3, (#4169⋊C3)⋊C3, …
maximal quotient of#66409⋊C3, C2×#4207⋊C3, #13091380, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 238);