Finite Group Databasebeta

D59×#1938 #28591427

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD59×#1938

Splittings

FittingC59×#1938 ⋊ C2
SylowC59 ⋊ C2×#1938

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1938C2
socleC22×C59C2×C4×D4
prime radicalC2×#41×D59C22
cosocleC22×C4×C59C24
hypercenter#1938D59
hypocenterC59C2×#1938
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1938

1074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 172306);