Finite Group Databasebeta

D59×#1533 #28556703

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

Aliases

direct productD59×#1533

Splittings

FittingC59×#1533 ⋊ C2
SylowC59 ⋊ C2×#1533

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#1533C2
socleC22×C59C22×C22⋊C4
prime radicalC22×D4×D59C4
cosocleC42×C59C24
hypercenter#1533D59
hypocenterC59C2×#1533
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1533

1310 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, 137582);