Finite Group Databasebeta

← Prev (#14412788) Next (#14412790) →

C2×C3×D5×#104 #14412789

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×D5×#104

Splittings

FittingC2×C3×C5×#104 ⋊ C2
HallC3×C5 ⋊ C22×#104
SylowC5 ⋊ C22×C3×#104

Subgroups

subgroupG/H
centerC2×C3×C4D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#104C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D5×#41C2
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×#104D5
hypocenterC5C22×C3×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

1712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

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, 138487);