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3−1+2⋊#170 #11761724

order1080
isoclinismisoclinic class of 3−1+2⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product3−1+2⋊#170
unambiguous semidirect product(C9⋊#170)⋊C3

Splittings

derivedC5×C9 ⋊ C3×C8
HallC5×3−1+2 ⋊ C8
Sylow3−1+2 ⋊ #170
SylowC5 ⋊ 3−1+2⋊C8

Subgroups

subgroupG/H
center, hypercenterC23−1+2⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C3×C8
FrattiniC2×C3C3×ΓL(1,𝔽16)
FittingC2×C5×3−1+2C4
socleC2×C3×C5C3×Dic3
prime radicalC2×C32×C5Dic3
cosocleC9×Dic5C2×C3
LCSG ▷ C5×C9
UCSC1 ◁ C2

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 360

Polycyclic presentation:

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

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 70);