Finite Group Databasebeta

← Prev (#14412207) Next (#14412209) →

C3×#10615843 #14412208

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

Aliases

direct productC3×#10615843

Splittings

HallC3×C5 ⋊ #2889
SylowC5 ⋊ C3×#2889

Subgroups

subgroupG/H
centerC2×C3C22×C22⋊Dic5
commutatorC22×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
Fitting, prime radicalC2×C3×C5×2−1+4C2
socleC2×C3×C5C22×C22⋊C4
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×2−1+4D5
hypocenterC5C3×#2889
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×#41 ◁ C2×C3×2−1+4

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137906);