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#14418126

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

Aliases

No aliases for this group.

Splittings

FittingC3×C5×AGL(1,ℤ/8) ⋊ C4
HallC3×C5 ⋊ #2956
SylowC5 ⋊ #84000
SylowC3 ⋊ #10617449

Subgroups

subgroupG/H
centerC2C2×D4×ΓL(1,𝔽16)
commutatorC3×C4×C5C23×C4
FrattiniC4C23×ΓL(1,𝔽16)
FittingC3×C5×AGL(1,ℤ/8)C4
socleC2×C3×C5C2×C4×D4
prime radicalC3×#66107C2
cosocleC3×C4×D5C24
hypercenterAGL(1,ℤ/8)ΓL(1,𝔽16)
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

916 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Polycyclic presentation:

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

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 143824);