Finite Group Databasebeta

D59×#1940 #28591956

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD59×#1940

Splittings

FittingC59×#1940 ⋊ C2
SylowC59 ⋊ C2×#1940

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#1940C2
prime radicalC23×D59C22×C4
cosocleC22×C4×C59C24
hypercenter#1940D59
hypocenterC59C2×#1940
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1940

1182 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, 172835);