Finite Group Databasebeta

← Prev (#14412794) Next (#14412796) →

C22×C3×#3969 #14412795

order1920
isoclinismisoclinic class of #686
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×C3×#3969

Splittings

HallC3×C5 ⋊ C22×#104
SylowC5 ⋊ C22×C3×#104

Subgroups

subgroupG/H
centerC22×C3×C4C22⋊D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
Fitting, prime radicalC22×C3×C5×#41C2
socleC23×C3×C5C22⋊C4
cosocleC2×C4×C5C24×C3
hypercenterC22×C3×#41D5
hypocenterC5C22×C3×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C23×C3×C4 ◁ C22×C3×#41

1712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138493);