Finite Group Databasebeta

C2×M32×Dic43 #25249226

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M32×Dic43

Splittings

SylowC43 ⋊ C2×C4×M32

Subgroups

subgroupG/H
centerC22×C8C22×D43
commutatorC2×C43C22×C4×C8
FrattiniC2×C8C23×D43
FittingC22×M32×C43C2
socleC23×C43C22×C8
prime radicalC24×C43C2×C8
cosocleC2×C8×C43C24
hypercenterC22×M32D43
hypocenterC43C2×C4×M32
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C22×M32

918 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322197);