Finite Group Databasebeta

C2×#20246256 #26375513

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#20246256

Splittings

FittingC2×C47×#389 ⋊ C2
SylowC47 ⋊ C2×#2344

Subgroups

subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#389C2
socleC24×C47C24
prime radicalC24×D47C23
cosocleC23×C47C25
hypercenterC2×#389D47
hypocenterC47C2×#2344
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

3526 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328803);