Finite Group Databasebeta

C2×C3×D5×#97 #14411191

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×D5×#97

Splittings

FittingC2×C3×C5×#97 ⋊ C2
HallC3×C5 ⋊ C22×#97
SylowC5 ⋊ C22×C3×#97

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC2×C5C22×C3×C42
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#97C2
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C2×C4
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×#97D5
hypocenterC5C22×C3×#97
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×#97

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 136889);