Finite Group Databasebeta

D59×#2216 #28743109

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD59×#2216

Splittings

FittingC59×#2216 ⋊ C2
SylowC59 ⋊ C2×#2216

Subgroups

subgroupG/H
centerC22C2×D8×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#2216C2
socleC22×C59C22×D8
prime radicalC23×D59D8
hypercenter#2216D59
hypocenterC59C2×#2216
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2216

702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323988);