Finite Group Databasebeta

D59×#1680 #28571069

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productD59×#1680

Splittings

FittingC59×#1680 ⋊ C2
SylowC59 ⋊ C2×#1680

Subgroups

subgroupG/H
centerC22#121×D59
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC59×#1680C2
socleC22×C59C2×#121
prime radicalC22×D59#121
hypercenter#1680D59
hypocenterC59C2×#1680
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #1680

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 151948);