Finite Group Databasebeta

D4×#14519703 #29695681

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

Aliases

direct productD4×#14519703

Splittings

FittingD4×M16×C61 ⋊ C2
SylowC61 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×M16×C61C2
socleC22×C61C22×C22⋊C4
prime radicalD4×#11758222C2
cosocleC22×C4×C61C24
hypercenterD4×M16D61
hypocenterC61D4×#104
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×M16

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

1570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 185236);