Finite Group Databasebeta

D59×#1781 #28587809

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productD59×#1781

Splittings

FittingC59×#1781 ⋊ C2
SylowC59 ⋊ C2×#1781

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC59×#1781C2
socleC22×C59C22×C22⋊C4
prime radicalC23×D4×D59C2
cosocleC24×C59C24
hypercenter#1781D59
hypocenterC59C2×#1781
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C25 ◁ #1781

6254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 944

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, 168688);