Finite Group Databasebeta

← Prev (#14478680) Next (#14478682) →

C23×C3×#685 #14478681

order1920
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×C3×#685

Splittings

FittingC24×C3×C4×C5 ⋊ C2
HallC3×C5 ⋊ C23×C22⋊C4
SylowC5 ⋊ C23×C3×C22⋊C4

Subgroups

subgroupG/H
centerC25×C3C2×D5
commutatorC2×C5C24×C3×C4
FrattiniC22C24×C3×D5
FittingC24×C3×C4×C5C2
socleC25×C3×C5C22
prime radicalC25×C3×D5C2
cosocleC22×C5C25×C3
hypercenterC24×C3×C4D5
hypocenterC5C23×C3×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C25×C3 ◁ C24×C3×C4

9264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 204379);