Finite Group Databasebeta

D59×#3417 #29495210

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

Aliases

direct productD59×#3417

Splittings

FittingC59×#3417 ⋊ C2
SylowC59 ⋊ C2×#3417

Subgroups

subgroupG/H
centerC2C22×D8×D59
commutator, cosocleC8×C59C25
FrattiniC8C24×D59
FittingC59×#3417C2
socleC2×C59C23×D8
hypercenter#3417D59
hypocenterC59C2×#3417
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ #41 ◁ #131 ◁ #3417

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 1076089);