Finite Group Databasebeta

D59×#1735 #28586086

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productD59×#1735

Splittings

FittingC59×#1735 ⋊ C2
SylowC59 ⋊ C2×#1735

Subgroups

subgroupG/H
centerC22×C4D4×D59
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC59×#1735C2
socleC23×C59C22×D4
prime radicalC24×D59D4
cosocleC22×C4×C59C24
hypercenter#1735D59
hypocenterC59C2×#1735
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ #1735

2398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 166965);