Finite Group Databasebeta

SD16×#11745664 #28560130

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productSD16×#11745664

Splittings

SylowC59 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC2×C4×SD16×C59C2
socleC22×C59C2×C4×D4
prime radicalC22×D4×C59C2×C4
cosocleC42×C59C24
hypercenterC2×C4×SD16D59
hypocenterC59M16×SD16
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×SD16

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 141009);