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#14294858

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

FittingC3×C5×M16 ⋊ C2×C4
HallC3×C5 ⋊ C2×#344
SylowC5 ⋊ D3×#344
SylowC3 ⋊ #10604771

Subgroups

subgroupG/H
centerC2D3×(C2×AGL(1,𝔽5))⋊C4
commutatorC22×C3×C5C2×C42
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×M16C2×C4
socleC2×C3×C5C2×#95
prime radicalC22×D3×D5C2×C4
cosocleC2×C3×C4×D5C23
hypercenterM16D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#344
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Polycyclic presentation:

2^7,3,5|a^2=e,b^2=f,f^2=g,b^a=bd,d^a=dg,i^a=i^3,e^b=eg,i^b=i^2,h^c=h^2,i^c=i^4,i^e=i^4,i^f=i^4

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20556);