Finite Group Databasebeta

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#14324433

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

No aliases for this group.

Splittings

FittingC2×C3×C5×D4 ⋊ C2×C4
HallC3×C5 ⋊ #2328
SylowC5 ⋊ #82329
SylowC3 ⋊ #10617368

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×D4C2×C4
prime radicalD5×#940C2
cosocleC22×C3×D5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#2328
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

1480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Polycyclic presentation:

2^7,3,5|a^2=g,b^2=eg,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,i^a=i^3,c^b=ce,i^b=i^2,h^c=h^2,i^g=i^4

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 50131);