Finite Group Databasebeta

← Prev (#14285588) Next (#14285590) →

C3×#10601213 #14285589

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10601213

Splittings

HallC3×C5 ⋊ #1565
SylowC5 ⋊ C3×#1565

Subgroups

subgroupG/H
centerC2×C3×C4C2×C22⋊D5
commutatorC4×C5C22×C3×C8
FrattiniC42C22×C3×D5
FittingC2×C3×C5×C4⋊C8C2
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×C5C4⋊C4
cosocleC42×C5C23×C3
hypercenterC2×C3×C4⋊C8D5
hypocenterC5C3×#1565
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 11287);