Finite Group Databasebeta

D59×#2901 #29452284

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD59×#2901

Splittings

FittingC59×#2901 ⋊ C2
SylowC59 ⋊ C2×#2901

Subgroups

subgroupG/H
centerC4C22×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC59×#2901C2
socleC2×C59C23×C22⋊C4
prime radical#585×D59C2
cosocleC2×C4×C59C25
hypercenter#2901D59
hypocenterC59C2×#2901
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C2×#41 ◁ #2901

4946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 944

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, 1033163);