Finite Group Databasebeta

C2×C3×#64772 #14294628

order1920
isoclinismisoclinic class of #677
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×C3×#64772

Splittings

HallC3×C5 ⋊ C2×#341
SylowC5 ⋊ C2×C3×#341

Subgroups

subgroupG/H
centerC22×C3×C4D20
commutatorC4×C5C2×C3×C42
FrattiniC22×C4C22×C3×D5
FittingC23×C3×C5×C8C2
socleC23×C3×C5C4⋊C4
prime radicalC24×C3×C5Q8
cosocleC22×C4×C5C23×C3
hypercenterC23×C3×C8D5
hypocenterC5C2×C3×#341
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C23×C3×C4 ◁ C23×C3×C8

784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20326);