Finite Group Databasebeta

C4×D8×Dic43 #25095062

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×D8×Dic43

Splittings

SylowC43 ⋊ C42×D8

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC2×C4×D8×C43C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
cosocleC22×C4×C43C24
hypercenterC2×C4×D8D43
hypocenterC43C42×D8
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

1350 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168033);