Finite Group Databasebeta

D59×#3415 #29495196

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD59×#3415

Splittings

FittingC59×#3415 ⋊ C2
SylowC59 ⋊ C2×#3415

Subgroups

subgroupG/H
centerC2C22×D8×D59
commutator, cosocleC8×C59C25
FrattiniC8C24×D59
FittingC59×#3415C2
socleC2×C59C23×D8
hypercenter#3415D59
hypocenterC59C2×#3415
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ #41 ◁ #131 ◁ #3415

2126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076075);