Finite Group Databasebeta

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#14297280

order1920
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

FittingC3×C5×H(5,𝔽2) ⋊ C4
HallC3×C5 ⋊ #1794
SylowC5 ⋊ #72146
SylowC3 ⋊ #10605016

Subgroups

subgroupG/H
centerC2#11752459
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×H(5,𝔽2)C4
socleC2×C3×C5#379
prime radicalC3×#66285C2
cosocleC2×C3×C4×D5C23
hypercenterH(5,𝔽2)ΓL(1,𝔽16)
hypocenterC3×C5#1794
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ H(5,𝔽2)

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Polycyclic presentation:

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

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 22978);