Finite Group Databasebeta

D59×#1726 #28586014

order15104
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C42

Aliases

direct productD59×#1726

Splittings

FittingC59×#1726 ⋊ C2
SylowC59 ⋊ C2×#1726

Subgroups

subgroupG/H
centerC22×C8C22×D59
commutatorC2×C59C2×C43
FrattiniC22×C4C23×D59
FittingC59×#1726C2
socleC23×C59C23×C4
prime radicalC23×D59C22×C4
cosocleC22×C4×C59C24
hypercenter#1726D59
hypocenterC59C2×#1726
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ #1726

1614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 166893);