Finite Group Databasebeta

D59×#1600 #28560876

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD59×#1600

Splittings

FittingC59×#1600 ⋊ C2
SylowC59 ⋊ C2×#1600

Subgroups

subgroupG/H
centerC22#120×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#1600C2
socleC22×C59C2×#120
hypercenter#1600D59
hypocenterC59C2×#1600
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1600

1716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 944

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, 141755);