Finite Group Databasebeta

C22×#91100 #14412285

order1920
isoclinismisoclinic class of #6706
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#91100

Splittings

HallC3×C5 ⋊ C22×#103
SylowC5 ⋊ C22×#816
SylowC3 ⋊ C22×#3948

Subgroups

subgroupG/H
centerC24D60
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC23×C3×C5×C8C2
socle, prime radicalC24×C3×C5D4
cosocleC2×C3×C4×C5C24
hypercenterC23×C8D15
hypocenterC3×C5C22×#103
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

1632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137983);