Finite Group Databasebeta

D4×#13063258 #25114710

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

Aliases

direct productD4×#13063258

Splittings

SylowC43 ⋊ D4×#107

Subgroups

subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×C4⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
cosocleC22×C4×C43C24
hypercenterD4×C4⋊C4D43
hypocenterC43D4×#107
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

1126 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 187681);