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C4⋊(C3⋊(C3⋊#170)) #13086305

order1440
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3

Aliases

unambiguous semidirect productC4⋊(C3⋊(C3⋊#170))

Splittings

HallC32×C5 ⋊ C4⋊C8
SylowC32 ⋊ C4⋊#170
SylowC5 ⋊ C4⋊(C3⋊(C3⋊C8))

Subgroups

subgroupG/H
center, FrattiniC22C2×C3⋊ΓL(1,𝔽16)
commutatorC2×C32×C5C2×C8
FittingC2×C32×C4×C5C4
socle, prime radicalC22×C32×C5C2×C4
cosocleC2×C32×Dic5C22
hypercenterC2×C4C3⋊ΓL(1,𝔽16)
hypocenterC32×C5C4⋊C8
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1440

Polycyclic presentation:

2^5,3^2,5|a^2=c,b^2=d,c^2=e,b^a=bd,f^a=f^2,g^a=g^2,h^a=h^2,h^c=h^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, 2622);