Finite Group Databasebeta

D59×#2155 #28741698

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD59×#2155

Splittings

FittingC59×#2155 ⋊ C2
SylowC59 ⋊ C2×#2155

Subgroups

subgroupG/H
centerC4#106×D59
commutatorC8×C59C23×C4
FrattiniC2×C8C23×D59
FittingC59×#2155C2
socleC2×C59C22×#106
prime radicalC23×D59SD16
cosocleC2×C8×C59C24
hypercenter#2155D59
hypocenterC59C2×#2155
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2155

658 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, 322577);