Finite Group Databasebeta

C2×#11751322 #14320777

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

Aliases

direct productC2×#11751322

Splittings

HallC3×C5 ⋊ C2×#390
SylowC5 ⋊ C2×#5221
SylowC3 ⋊ C2×#65510

Subgroups

subgroupG/H
centerC24C22×D15
commutatorC22×C3×C5C23×C4
FrattiniC23C23×D15
Fitting, prime radicalC23×C3×C5×D4C2
socleC24×C3×C5C23
cosocleC23×C3×C5C24
hypercenterC23×D4D15
hypocenterC3×C5C2×#390
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×D4

2720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 46475);