Finite Group Databasebeta

← Prev (#14478772) Next (#14478774) →

C2×C3×C4×D4×D5 #14478773

order1920
automorphism?
homologyAbelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×C3×C4×D4×D5

Splittings

FittingC2×C3×C4×C5×D4 ⋊ C2
HallC3×C5 ⋊ C22×C4×D4
SylowC5 ⋊ C22×C3×C4×D4

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC2×C5C24×C3×C4
FrattiniC22C24×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC22×C3×D4×D5C2
cosocleC22×C5C25×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C22×C3×C4×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×D4

5056 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204471);