Finite Group Databasebeta

C4×C5×#812 #14312584

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

Aliases

direct productC4×C5×#812

Splittings

HallC3×C5 ⋊ C4×M32
SylowC3 ⋊ C4×C5×M32

Subgroups

subgroupG/H
centerC4×C5×C8C2×D3
commutatorC2×C3C2×C4×C5×C8
FrattiniC2×C8C22×C5×D3
FittingC2×C3×C4×C5×C8C2
socleC22×C3×C5C22×C8
prime radicalC23×C3×C5C2×C8
cosocleC2×C3×C8C23×C5
hypercenterC2×C4×C5×C8D3
hypocenterC3C4×C5×M32
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5×C8 ◁ C2×C4×C5×C8

392 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, 38282);