Finite Group Databasebeta

C2×C3×#65382 #14437687

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

Aliases

direct productC2×C3×#65382

Splittings

HallC3×C5 ⋊ C2×#487
SylowC5 ⋊ C2×C3×#487

Subgroups

subgroupG/H
centerC23×C3C2×C22⋊D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×C4⋊Q8C2
socle, prime radicalC23×C3×C5C2×D4
hypercenterC2×C3×C4⋊Q8D5
hypocenterC5C2×C3×#487
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊Q8

848 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, 163385);