Finite Group Databasebeta

D59×#2112 #28741355

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD59×#2112

Splittings

FittingC59×#2112 ⋊ C2
SylowC59 ⋊ C2×#2112

Subgroups

subgroupG/H
center, FrattiniC2×C8C23×D59
commutator, socleC22×C59C23×C8
FittingC59×#2112C2
prime radicalC24×D59C8
cosocleC2×C8×C59C24
hypercenter#2112D59
hypocenterC59C2×#2112
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ #2112

1406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322234);