Finite Group Databasebeta

C3×C42×Dic10 #14319614

order1920
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC3×C42×Dic10

Splittings

HallC3×C5 ⋊ C42×Q8
SylowC5 ⋊ C3×C42×Q8

Subgroups

subgroupG/H
centerC2×C3×C42C2×D5
commutatorC2×C5C22×C3×C42
FrattiniC23C23×C3×D5
FittingC3×C43×C5C2
socle, prime radicalC23×C3×C5C24
cosocleC23×C5C24×C3
hypercenterC3×C43D5
hypocenterC5C3×C42×Q8
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C42 ◁ C3×C43

1368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45312);