Finite Group Databasebeta

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C3×#10605369 #14327670

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×#10605369

Splittings

FittingC3×C4×C5×C4⋊C4 ⋊ C2
HallC3×C5 ⋊ #2354
SylowC5 ⋊ C3×#2354

Subgroups

subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C4⋊C4C2
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
cosocleC23×C5C24×C3
hypercenterC3×C4×C4⋊C4D5
hypocenterC5C3×#2354
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4

1264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 53368);