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Cayley diagram

#6880⋊C2 #92193

order486
isoclinismisoclinic class of #6880⋊C2
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#6880⋊C2

Splittings

Fitting, Sylow#6880 ⋊ C2

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#733C2×C3
FrattiniC3×C9C3×D3
Fitting#6880C2
socleC3#4178
prime radical#733⋊C2C3
LCSG ▷ #733
UCSC1

30 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:

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

Polycyclic presentation:

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

Conjugacy classes & character table

31 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#6880⋊C2, #10624536⋊C2, #13090590, …
maximal normal subgroup ofC2×#6880⋊C2, C3×#6880⋊C2, (#6880⋊C2)⋊C3
maximal quotient of#6880⋊C4, C2×#6880⋊C2, #10624482⋊C2, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 38);