Finite Group Databasebeta

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Dic5×#940 #14322265

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

Aliases

direct productDic5×#940

Splittings

HallC3×C5 ⋊ C4×#127
SylowC5 ⋊ C4×#940
SylowC3 ⋊ Dic5×#127

Subgroups

subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#940C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C4×#127
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

1848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 47963);