Finite Group Databasebeta

SD16×C22⋊#6923 #30620210

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productSD16×C22⋊#6923

Splittings

FittingC22×SD16×C61 ⋊ C4
SylowC61 ⋊ C22⋊C4×SD16

Subgroups

subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC22×SD16×C61C4
socleC22×C61C2×C4×D4
prime radicalC22×D4×D61C22
cosocleC2×C4×D61C24
hypercenterC22×SD16#6923
hypocenterC61C22⋊C4×SD16
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

1614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1109765);