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C4⋊(C3⋊(C3⋊#168)) #13085087

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

Aliases

unambiguous semidirect productC4⋊(C3⋊(C3⋊#168))

Splittings

HallC32×C5 ⋊ C4⋊C8
SylowC32 ⋊ C4⋊#168
SylowC5 ⋊ C4⋊(C3⋊(C3⋊C8))

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×C3⋊D15
commutatorC2×C32×C5C2×C8
FittingC32×C42×C5C2
socle, prime radicalC22×C32×C5C2×C4
cosocleC2×C32×C4×C5C22
hypercenterC42C3⋊D15
hypocenterC32×C5C4⋊C8
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2×C4 ◁ C42

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1440

Polycyclic presentation:

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

Conjugacy classes & character table

372 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1404);