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Cayley diagram

#6883⋊C2 #92196

order486
isoclinismisoclinic class of #6883⋊C2
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#6883⋊C2

Splittings

Fitting, Sylow#6883 ⋊ C2

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#732C2×C3
FrattiniC3×C9C3×D3
Fitting#6883C2
socleC3#4178
prime radical#4185C3
LCSG ▷ #732
UCSC1

31 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:

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

Polycyclic presentation:

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

Conjugacy classes & character table

23 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#6883⋊C2, C3×#6883⋊C2, C3⋊(#6883⋊C2), …
maximal normal subgroup ofC2×#6883⋊C2, C3×#6883⋊C2, #92191⋊C3
maximal quotient of#6883⋊C4, C2×#6883⋊C2, #10624482⋊C2, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 41);