Finite Group Databasebeta

C22×#15688878 #26213629

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C28

Aliases

direct productC22×#15688878

Splittings

SylowC47 ⋊ C22×#336

Subgroups

subgroupG/H
centerC24×C4C2×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC23×C42×C47C2
socle, prime radicalC25×C47C2×C4
cosocleC22×C4×C47C24
hypercenterC23×C42D47
hypocenterC47C22×#336
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C24×C4 ◁ C23×C42

3086 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 166919);