Finite Group Databasebeta

D59×#2120 #28741406

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD59×#2120

Splittings

FittingC59×#2120 ⋊ C2
SylowC59 ⋊ C2×#2120

Subgroups

subgroupG/H
centerC4#99×D59
commutatorC23×C59C23×C4
FrattiniC2×D4C23×D59
FittingC59×#2120C2
socleC2×C59C22×#99
prime radical#525×D59C2
cosocleC2×D4×C59C24
hypercenter#2120D59
hypocenterC59C2×#2120
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2120

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 944

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322285);