Finite Group Databasebeta

D59×#1789 #28587930

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD59×#1789

Splittings

FittingC59×#1789 ⋊ C2
SylowC59 ⋊ C2×#1789

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1789C2
socleC22×C59C22×C22⋊C4
prime radicalC22×#41×D59C2
cosocleC22×C4×C59C24
hypercenter#1789D59
hypocenterC59C2×#1789
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

4102 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, 168809);