Finite Group Databasebeta

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#14321917

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

Aliases

No aliases for this group.

Splittings

HallC3×C5 ⋊ C4×C22⋊Q8
SylowC5 ⋊ #73866
SylowC3 ⋊ AGL(1,𝔽5)×C22⋊Q8

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×C22⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

1312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Polycyclic presentation:

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

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 47615);