Finite Group Databasebeta

C2×C3×#64938 #14319429

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C3×#64938

Splittings

HallC3×C5 ⋊ C2×C4×C4⋊C4
SylowC5 ⋊ C2×C3×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24×C3C22×D5
commutatorC2×C5C22×C3×C42
FrattiniC23C23×C3×D5
FittingC2×C3×C5×#95C2
socle, prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC2×C3×#95D5
hypocenterC5C2×C3×C4×C4⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

1856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45127);