Finite Group Databasebeta

C22×#15688969 #26374448

order12032
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C42

Aliases

direct productC22×#15688969

Splittings

SylowC47 ⋊ C22×#376

Subgroups

subgroupG/H
centerC24×C4C2×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC23×C42×C47C2
socle, prime radicalC25×C47C23
cosocleC23×C47C25
hypercenterC23×C42D47
hypocenterC47C22×#376
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C24×C4 ◁ C23×C42

5150 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, 327738);