Finite Group Databasebeta

D59×#1305 #28479017

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD59×#1305

Splittings

FittingC59×#1305 ⋊ C2
SylowC59 ⋊ C2×#1305

Subgroups

subgroupG/H
centerC22#95×D59
commutatorC23×C59C2×C42
FrattiniC23×C4C22×D59
FittingC59×#1305C2
socleC22×C59C2×#95
prime radicalC24×D59C2×C4
cosocleC23×C4×C59C23
hypercenter#1305D59
hypocenterC59C2×#1305
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 59896);