Finite Group Databasebeta

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C4×C5×#888 #14322300

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

Aliases

direct productC4×C5×#888

Splittings

HallC3×C5 ⋊ C4×C4⋊Q8
SylowC3 ⋊ C4×C5×C4⋊Q8

Subgroups

subgroupG/H
centerC22×C4×C5C22×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C4×C5×C4⋊C4C2
socle, prime radicalC23×C3×C5C24
cosocleC23×C3C24×C5
hypercenterC4×C5×C4⋊C4D3
hypocenterC3C4×C5×C4⋊Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C4×C5×C4⋊C4

1176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 47998);