Finite Group Databasebeta

C23×C5×#217 #14478683

order1920
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C24×C4×C5 · Schur multiplier (H2) = C211

Aliases

direct productC23×C5×#217

Splittings

HallC3×C5 ⋊ C23×C22⋊C4
SylowC3 ⋊ C23×C5×C22⋊C4

Subgroups

subgroupG/H
centerC25×C5C2×D3
commutatorC2×C3C24×C4×C5
FrattiniC22C24×C5×D3
Fitting, prime radicalC26×C3×C5C2
socleC25×C3×C5C22
cosocleC22×C3C25×C5
hypercenterC26×C5D3
hypocenterC3C23×C5×C22⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C25×C5 ◁ C26×C5

9264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204381);