Finite Group Databasebeta

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C3⋊#4626 #10590112

order576
isoclinismisoclinic class of C3⋊#4626
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C3×C4

Aliases

unambiguous semidirect productC3⋊#4626

Splittings

derivedC3×C42⋊C3 ⋊ C4

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, hypocenterC3×C42⋊C3C4
FrattiniC23C3⋊S4
FittingC3×#127D3
socleC22×C3SL(2,ℤ/4)
prime radical, cosocleC3×#127⋊C3C2
LCSG ▷ C3×C42⋊C3
UCSC1

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Polycyclic presentation:

2^2,3^2,2^4|a^2=b,e^2=g,f^2=gh,c^a=c^2,d^a=d^2,e^a=f,f^a=eg,g^a=gh,e^b=eg,f^b=fgh,e^c=fg,f^c=ef,g^c=gh,h^c=g

Conjugacy classes & character table

21 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#4626, (#857⋊C2)⋊D3, C2×C3⋊#4626, …
maximal normal subgroup ofD3×#4626, (#857⋊C2)⋊D3, C2×C3⋊#4626, …
maximal quotient ofC3⋊#67999, C3⋊#68000, C3⋊#68003, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 1994);