Finite Group Databasebeta

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C3×#10602362 #14280265

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10602362

Splittings

HallC3×C5 ⋊ #1445
SylowC5 ⋊ C3×#1445

Subgroups

subgroupG/H
centerC24×C3C22×D5
commutatorC23×C5C22×C3×C4
FrattiniC24C22×C3×D5
FittingC22×C3×C5×C4⋊C4C2
socle, prime radicalC24×C3×C5C23
cosocleC24×C5C23×C3
hypercenterC22×C3×C4⋊C4D5
hypocenterC5C3×#1445
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C4⋊C4

1040 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 5963);