Finite Group Databasebeta

D59×#1985 #28593132

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD59×#1985

Splittings

FittingC59×#1985 ⋊ C2
SylowC59 ⋊ C2×#1985

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#1985C2
prime radicalC23×D59C22×C4
cosocleC22×C4×C59C24
hypercenter#1985D59
hypocenterC59C2×#1985
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1985

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 174011);