Finite Group Databasebeta

D4×SD16×D59 #29463897

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD4×SD16×D59

Splittings

FittingD4×SD16×C59 ⋊ C2
SylowC59 ⋊ C2×D4×SD16

Subgroups

subgroupG/H
centerC22C22×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingD4×SD16×C59C2
socleC22×C59C23×D4
prime radicalD42×D59C2
hypercenterD4×SD16D59
hypocenterC59C2×D4×SD16
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×SD16

3226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1085 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1044776);