Finite Group Databasebeta

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#14278685

order1920
automorphism?
homologyAbelianization (H1) = C4×C16 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

FittingC2×C3×C5×C16 ⋊ C4
HallC3×C5 ⋊ #1374
SylowC5 ⋊ #67804
SylowC3 ⋊ (C2×AGL(1,𝔽5))⋊C16

Subgroups

subgroupG/H
center, FrattiniC2×C8C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C4×C16
FittingC2×C3×C5×C16C4
socleC22×C3×C5C4×C8
prime radicalC22×C3×D5C2×C8
cosocleC2×C3×C8×D5C22
hypercenterC2×C16ΓL(1,𝔽16)
hypocenterC3×C5#1374
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C8 ◁ C2×C16

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Polycyclic presentation:

2^7,3,5|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,h^b=h^2,i^b=i^2,i^e=i^4

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4383);