Finite Group Databasebeta

C22×#91094 #14412279

order1920
isoclinismisoclinic class of #6715
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#91094

Splittings

HallC3×C5 ⋊ C22×#103
SylowC5 ⋊ C22×#810
SylowC3 ⋊ C22×#3942

Subgroups

subgroupG/H
centerC24#1220
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC22×C3×C5×C4⋊C4C2
socle, prime radicalC24×C3×C5D4
cosocleC2×C3×C4×C5C24
hypercenterC22×C4⋊C4D15
hypocenterC3×C5C22×#103
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

1632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137977);