Finite Group Databasebeta

C2×C3×#64686 #14312706

order1920
isoclinismisoclinic class of #64686
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22

Aliases

direct productC2×C3×#64686

Splittings

HallC3×C5 ⋊ C2×#347
SylowC5 ⋊ C2×C3×#347

Subgroups

subgroupG/H
centerC2×C3×C4C4×Dic5
commutatorC4×C5C2×C3×C42
FrattiniC2×C8C22×C3×D5
FittingC2×C3×C5×#97C2
socleC22×C3×C5#97
prime radicalC23×C3×C5M16
cosocleC2×C5×C8C23×C3
hypercenterC2×C3×#97D5
hypocenterC5C2×C3×#347
LCSG ▷ C4×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×#97

336 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, 38404);