Finite Group Databasebeta

D59×#2034 #28616149

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

Aliases

direct productD59×#2034

Splittings

FittingC59×#2034 ⋊ C2
SylowC59 ⋊ C2×#2034

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2034C2
socleC23×C59C22×D4
prime radicalC2×#121×D59C2
hypercenter#2034D59
hypocenterC59C2×#2034
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

2006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 197028);