Finite Group Databasebeta

D59×#2399 #28754965

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productD59×#2399

Splittings

FittingC59×#2399 ⋊ C2
SylowC59 ⋊ C2×#2399

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutator, socle, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC59×#2399C2
prime radicalC23×D59C24
hypercenter#2399D59
hypocenterC59C2×#2399
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #2399

2814 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, 335844);