Finite Group Databasebeta

D4×#13063253 #25112272

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#13063253

Splittings

FittingC42×D4×C43 ⋊ C2
SylowC43 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC42×D4×C43C2
socleC22×C43C22×C22⋊C4
prime radicalD4×#10621898C2
cosocleC22×C4×C43C24
hypercenterC42×D4D43
hypocenterC43D4×#104
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ C42×D4

1608 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 185243);