Finite Group Databasebeta

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C5×Dic3×#127 #14322254

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25×C4

Aliases

direct productC5×Dic3×#127

Splittings

HallC3×C5 ⋊ C4×#127
SylowC3 ⋊ C4×C5×#127

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
Fitting, prime radicalC2×C3×C5×#127C2
socleC23×C3×C5C24
cosocleC23×C3C24×C5
hypercenterC2×C5×#127D3
hypocenterC3C4×C5×#127
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C5×#127

1848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 47952);