Finite Group Databasebeta

C22×#15688901 #26368932

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productC22×#15688901

Splittings

SylowC47 ⋊ C22×#347

Subgroups

subgroupG/H
centerC22×C4C4×Dic47
commutatorC4×C47C22×C42
FrattiniC2×C8C23×D47
FittingC22×#97×C47C2
socleC23×C47#97
prime radicalC24×C47M16
cosocleC2×C8×C47C24
hypercenterC22×#97D47
hypocenterC47C22×#347
LCSG ▷ C4×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×#97

782 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322222);