Finite Group Databasebeta

D59×#1500 #28555773

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD59×#1500

Splittings

FittingC59×#1500 ⋊ C2
SylowC59 ⋊ C2×#1500

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1500C2
socleC22×C59C22×C22⋊C4
prime radical#121×D59C22
cosocleC22×C4×C59C24
hypercenter#1500D59
hypocenterC59C2×#1500
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1500

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 136652);