Finite Group Databasebeta

D59×#1759 #28586403

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productD59×#1759

Splittings

FittingC59×#1759 ⋊ C2
SylowC59 ⋊ C2×#1759

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC59×#1759C2
socleC22×C59C22×C22⋊C4
prime radicalC2×#41×D59C22
cosocleC22×C4×C59C24
hypercenter#1759D59
hypocenterC59C2×#1759
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

1662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 167282);