Finite Group Databasebeta

D59×#1747 #28586190

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productD59×#1747

Splittings

FittingC59×#1747 ⋊ C2
SylowC59 ⋊ C2×#1747

Subgroups

subgroupG/H
centerC8C42×D59
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC59×#1747C2
socleC2×C59C2×#376
prime radicalC23×D59#41
cosocleC22×C4×C59C24
hypercenter#1747D59
hypocenterC59C2×#1747
LCSG ▷ C4×C59 ▷ C59
UCSC1 ◁ C8 ◁ #1747

930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 167069);