Finite Group Databasebeta

D4×#13063236 #25095057

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productD4×#13063236

Splittings

SylowC43 ⋊ D4×#97

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C22×C42
FittingC42×D4×C43C2
socleC23×C43C23×C4
prime radicalC22×D4×C43C2×C4
cosocleC22×C4×C43C24
hypercenterC42×D4D43
hypocenterC43D4×#97
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C42×D4

1274 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168028);