Finite Group Databasebeta

D59×#2064 #28617225

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

Aliases

direct productD59×#2064

Splittings

FittingC59×#2064 ⋊ C2
SylowC59 ⋊ C2×#2064

Subgroups

subgroupG/H
centerC22#121×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2064C2
socleC22×C59C2×#121
prime radicalC23×D59#41
hypercenter#2064D59
hypocenterC59C2×#2064
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2064

1006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 198104);