Finite Group Databasebeta

C2×C5×#4549 #14312795

order1920
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C5×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×C5×#4549

Splittings

HallC3×C5 ⋊ C2×C22⋊C16
SylowC3 ⋊ C2×C5×C22⋊C16

Subgroups

subgroupG/H
centerC22×C5×C8C2×D3
commutatorC2×C3C22×C5×C16
FrattiniC2×C8C22×C5×D3
FittingC23×C3×C5×C8C2
socleC23×C3×C5C2×C8
prime radicalC24×C3×C5C8
cosocleC2×C3×C8C23×C5
hypercenterC23×C5×C8D3
hypocenterC3C2×C5×C22⋊C16
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5×C8 ◁ C23×C5×C8

544 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, 38493);