Finite Group Databasebeta

M32×Dic86 #25250110

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct productM32×Dic86

Splittings

SylowC43 ⋊ Q8×M32

Subgroups

subgroupG/H
center, FrattiniC2×C8C23×D43
commutator, socleC22×C43C23×C8
FittingC4×M32×C43C2
prime radicalC23×C43C22×C8
cosocleC2×C8×C43C24
hypercenterC4×M32D43
hypocenterC43Q8×M32
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C4×M32

530 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, 323081);