Finite Group Databasebeta

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C4×C5×#833 #14295416

order1920
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C5×#833

Splittings

HallC3×C5 ⋊ C4×#100
SylowC3 ⋊ C4×C5×#100

Subgroups

subgroupG/H
centerC2×C4×C5#217
commutatorC22×C3C2×C42×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C4×C5×D4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C5×D4C22
cosocleC22×C3×C4C23×C5
hypercenterC2×C4×C5×D4D3
hypocenterC3C4×C5×#100
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ C2×C4×C5×D4

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21114);