Finite Group Databasebeta

D59×#1565 #28557664

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productD59×#1565

Splittings

FittingC59×#1565 ⋊ C2
SylowC59 ⋊ C2×#1565

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC4×C59C23×C8
FrattiniC42C23×D59
FittingC59×#1565C2
socleC22×C59C22×C4⋊C4
prime radicalC23×D59C4⋊C4
cosocleC42×C59C24
hypercenter#1565D59
hypocenterC59C2×#1565
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 138543);