Finite Group Databasebeta

C2×C3×#65473 #14416417

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C3×#65473

Splittings

HallC3×C5 ⋊ C2×#441
SylowC5 ⋊ C2×C3×#441

Subgroups

subgroupG/H
centerC23×C3D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC22×C3×C5×Q16C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC2×C4×C5C24×C3
hypercenterC22×C3×Q16D5
hypocenterC5C2×C3×#441
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×Q16

960 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142115);