Finite Group Databasebeta

C22×#15688908 #26368976

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#15688908

Splittings

FittingC22×M32×C47 ⋊ C2
SylowC47 ⋊ C22×#350

Subgroups

subgroupG/H
centerC22×C8C22⋊D47
commutatorC4×C47C23×C8
FrattiniC2×C8C23×D47
FittingC22×M32×C47C2
socleC23×C47C22⋊C8
prime radicalC22×#10625350C4
cosocleC2×C8×C47C24
hypercenterC22×M32D47
hypocenterC47C22×#350
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C22×M32

1174 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322266);