Finite Group Databasebeta

← Prev (#14280102) Next (#14280104) →

#14280103

order1920
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

FittingC2×C3×C5×C22⋊C4 ⋊ C4
HallC3×C5 ⋊ #1440
SylowC5 ⋊ #71548
SylowC3 ⋊ #10604255

Subgroups

subgroupG/H
center, FrattiniC23C22×ΓL(1,𝔽16)
commutator, socleC23×C3×C5C22×C4
FittingC2×C3×C5×C22⋊C4C4
prime radicalC24×C3×D5C22
cosocleC23×C3×D5C23
hypercenterC2×C22⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1440
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

1472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Polycyclic presentation:

2^7,3,5|a^2=g,c^2=d,b^a=bd,c^a=ce,h^a=h^2,i^a=i^2,c^b=cf,i^g=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, 5801);