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3−1+2⋊Dic5 #10587363

order540
isoclinismisoclinic class of C5⋊AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product3−1+2⋊Dic5
unambiguous semidirect productDic45⋊C3

Splittings

derivedC5×C9 ⋊ C3×C4
HallC5×3−1+2 ⋊ C4
Sylow3−1+2 ⋊ Dic5
SylowC5 ⋊ 3−1+2⋊C4

Subgroups

subgroupG/H
center, hypercenterC2C5⋊AGL(1,ℤ/9)
commutator, hypocenterC5×C9C3×C4
FrattiniC2×C3C3×D15
FittingC2×C5×3−1+2C2
socleC2×C3×C5C3×D3
prime radicalC2×C32×C5D3
cosocleC2×C5×C9C2×C3
LCSG ▷ C5×C9
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Polycyclic presentation:

2,3,2,3,5,3|a^2=c,d^3=f^2,d^a=d^2f,e^a=e^4,f^a=f^2,d^b=df

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#67077⋊C3, Dic5×AGL(1,ℤ/9), D5×3−1+2⋊C4, …
maximal normal subgroup of#67077⋊C3, Dic5×AGL(1,ℤ/9), D5×3−1+2⋊C4, …
maximal quotient of3−1+2⋊#168, C2×3−1+2⋊Dic5, #13108131, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(540, 23);