Finite Group Databasebeta

C3×#10610212 #14419587

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC3×#10610212

Splittings

FittingC2×C3×C5×#97 ⋊ C2
HallC3×C5 ⋊ #2968
SylowC5 ⋊ C3×#2968

Subgroups

subgroupG/H
centerC2×C3×C4C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×#97C2
socleC22×C3×C5C23×C4
prime radicalC3×#4076C4
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×#97D5
hypocenterC5C3×#2968
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×#97

744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 145285);