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C4⋊(C9⋊#170) #13083990

order1440
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productC4⋊(C9⋊#170)

Splittings

HallC5×C9 ⋊ C4⋊C8
SylowC9 ⋊ C4⋊#170
SylowC5 ⋊ C4⋊(C9⋊C8)

Subgroups

subgroupG/H
centerC22C2×C9⋊AGL(1,𝔽5)
commutatorC2×C5×C9C2×C8
FrattiniC22×C3C2×ΓL(1,𝔽16)
FittingC2×C4×C5×C9C4
socle, prime radicalC22×C3×C5C2×Dic3
cosocleC2×C9×Dic5C22
hypercenterC2×C4C9⋊AGL(1,𝔽5)
hypocenterC5×C9C4⋊C8
LCSG ▷ C2×C5×C9 ▷ C5×C9
UCSC1 ◁ C22 ◁ C2×C4

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1440

Polycyclic presentation:

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

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 307);