Finite Group Databasebeta

← Prev (#14295644) Next (#14295646) →

#14295645

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

No aliases for this group.

Splittings

FittingC3×C4×C5×Q8 ⋊ C4
HallC3×C5 ⋊ #1759
SylowC5 ⋊ #71643
SylowC3 ⋊ #10604450

Subgroups

subgroupG/H
centerC22C2×#6763
commutatorC3×C4×C5C2×C42
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C4×C5×Q8C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#713C22
cosocleC2×C3×C4×D5C23
hypercenterC4×Q8ΓL(1,𝔽16)
hypocenterC3×C5#1759
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Polycyclic presentation:

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21343);