Finite Group Databasebeta

D59×#1609 #28560825

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

Aliases

direct productD59×#1609

Splittings

FittingC59×#1609 ⋊ C2
SylowC59 ⋊ C2×#1609

Subgroups

subgroupG/H
centerC22#120×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#1609C2
socleC22×C59C2×#120
prime radical#121×D59C22
hypercenter#1609D59
hypocenterC59C2×#1609
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1609

1060 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 141704);