Finite Group Databasebeta

D59×#1786 #28587866

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

Aliases

direct productD59×#1786

Splittings

FittingC59×#1786 ⋊ C2
SylowC59 ⋊ C2×#1786

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1786C2
socleC23×C59C22×D4
prime radicalC23×D4×D59C2
cosocleC22×C4×C59C24
hypercenter#1786D59
hypocenterC59C2×#1786
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

6086 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, 168745);