Finite Group Databasebeta

C4×C5×#830 #14294997

order1920
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C2×C4×C5×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×C5×#830

Splittings

HallC3×C5 ⋊ C4×C22⋊C8
SylowC3 ⋊ C4×C5×C22⋊C8

Subgroups

subgroupG/H
centerC2×C42×C5C2×D3
commutatorC2×C3C2×C4×C5×C8
FrattiniC22×C4C22×C5×D3
FittingC22×C3×C42×C5C2
socleC23×C3×C5C22×C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C3×C4C23×C5
hypercenterC22×C42×C5D3
hypocenterC3C4×C5×C22⋊C8
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C42×C5 ◁ C22×C42×C5

872 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, 20695);