Finite Group Databasebeta

D59×#2007 #28615646

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productD59×#2007

Splittings

FittingC59×#2007 ⋊ C2
SylowC59 ⋊ C2×#2007

Subgroups

subgroupG/H
centerC22#120×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2007C2
socleC22×C59C2×#120
prime radical#537×D59C2
hypercenter#2007D59
hypocenterC59C2×#2007
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2007

2038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 196525);