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#13086296

order1440
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3

Aliases

No aliases for this group.

Splittings

FittingC32×C5×C8 ⋊ C4
HallC32×C5 ⋊ #107
SylowC32 ⋊ #3994
SylowC5 ⋊ #63645

Subgroups

subgroupG/H
centerC2C4⋊(C3⋊ΓL(1,𝔽16))
commutatorC32×C4×C5C2×C4
FrattiniC4C2×C3⋊ΓL(1,𝔽16)
FittingC32×C5×C8C4
socleC2×C32×C5C4⋊C4
prime radicalC2×C32×D5D4
cosocleC32×C4×D5C22
hypercenterC8C3⋊ΓL(1,𝔽16)
hypocenterC32×C5#107
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 360

Polycyclic presentation:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2613);