Finite Group Databasebeta

← Prev (#14412045) Next (#14412047) →

C22×#91117 #14412046

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#91117

Splittings

HallC3×C5 ⋊ C22×#100
SylowC5 ⋊ C22×#833
SylowC3 ⋊ C22×#3965

Subgroups

subgroupG/H
centerC23#6719
commutatorC22×C3×C5C23×C4
FrattiniC2×C4C23×D15
Fitting, prime radicalC23×C3×C5×D4C2
socleC23×C3×C5C22⋊C4
cosocleC2×C3×C4×C5C24
hypercenterC23×D4D15
hypocenterC3×C5C22×#100
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

1984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137744);