Finite Group Databasebeta

C22×#15688889 #26213705

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productC22×#15688889

Splittings

SylowC47 ⋊ C22×#342

Subgroups

subgroupG/H
centerC24(C2×D47)⋊C4
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC23×C22⋊C4×C47C2
socleC24×C47C22⋊C4
prime radicalC26×C47C22
cosocleC24×C47C24
hypercenterC23×C22⋊C4D47
hypocenterC47C22×#342
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C26 ◁ C23×C22⋊C4

4334 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, 166995);