Finite Group Databasebeta

← Prev (#92285) Next (#92287) →

Cayley diagram

#4179⋊C3 #92286

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

Aliases

unambiguous semidirect product#4179⋊C3

Splittings

Fitting, Sylow#6911 ⋊ C2
derivedC3×C9 ⋊ C2×C32

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×C9C2×C32
FrattiniC32C32×D3
Fitting#6911C2
socleC3C3×(C3⋊D3)⋊C3
LCSG ▷ C3×C9
UCSC1

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 27 points:

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

Polycyclic presentation:

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

Conjugacy classes & character table

31 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#4178⋊C2)⋊C3, C2×#4179⋊C3, #13091110, …
maximal normal subgroup of(#4178⋊C2)⋊C3, C2×#4179⋊C3, (#4169⋊C3)⋊C3, …
maximal quotient of#66326⋊C3, C2×#4179⋊C3, #13090732, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 131);