Finite Group Databasebeta

C2×C3×#64936 #14320709

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×#64936

Splittings

HallC3×C5 ⋊ C2×#389
SylowC5 ⋊ C2×C3×#389

Subgroups

subgroupG/H
centerC24×C3C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C5×#95C2
socle, prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC2×C3×#95D5
hypocenterC5C2×C3×#389
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

1600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 46407);