Finite Group Databasebeta

C2×C3×#65504 #14412381

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C3×#65504

Splittings

HallC3×C5 ⋊ C2×#418
SylowC5 ⋊ C2×C3×#418

Subgroups

subgroupG/H
centerC23×C3C2×C22⋊D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
Fitting, prime radicalC23×C3×C5×D4C2
socleC23×C3×C5C2×D4
cosocleC2×C4×C5C24×C3
hypercenterC23×C3×D4D5
hypocenterC5C2×C3×#418
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C23×C3×D4

2016 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 138079);