Finite Group Databasebeta

C2×C3×C5⋊#401 #14332588

order1920
isoclinismisoclinic class of #64945
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC2×C3×C5⋊#401
unambiguous semidirect product(C2×C5)⋊(C3×#401)

Splittings

HallC3×C5 ⋊ C2×#401
SylowC5 ⋊ C2×C3×#401

Subgroups

subgroupG/H
centerC24×C3C22×D5
commutator, cosocleC23×C5C24×C3
FrattiniC23C23×C3×D5
FittingC2×C3×C5×#95C2
socle, prime radicalC24×C3×C5C23
hypercenterC2×C3×#95D5
hypocenterC5C2×C3×#401
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

1032 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 58286);