Finite Group Databasebeta

C23×C3×C22⋊Dic5 #14478684

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

Aliases

direct productC23×C3×C22⋊Dic5

Splittings

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

Subgroups

subgroupG/H
centerC25×C3C2×D5
commutatorC2×C5C24×C3×C4
FrattiniC22C24×C3×D5
Fitting, prime radicalC26×C3×C5C2
socleC25×C3×C5C22
cosocleC22×C5C25×C3
hypercenterC26×C3D5
hypocenterC5C23×C3×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C25×C3 ◁ C26×C3

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, 204382);