Finite Group Databasebeta

D59×#1653 #28564501

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD59×#1653

Splittings

FittingC59×#1653 ⋊ C2
SylowC59 ⋊ C2×#1653

Subgroups

subgroupG/H
centerC22#120×D59
commutator, cosocleC42×C59C24
FrattiniC42C23×D59
FittingC59×#1653C2
socleC22×C59C2×#120
prime radicalC22×D59#120
hypercenter#1653D59
hypocenterC59C2×#1653
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #1653

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 145380);