Finite Group Databasebeta

C2×#20241523 #26136462

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20241523

Splittings

SylowC47 ⋊ C2×#1398

Subgroups

subgroupG/H
centerC2×C8C4×Dic47
commutatorC4×C47C2×C4×C8
FrattiniC2×C16C22×D47
FittingC2×C47×M64C2
socleC22×C47#346
prime radicalC23×C47M32
cosocleC2×C16×C47C23
hypercenterC2×M64D47
hypocenterC47C2×#1398
LCSG ▷ C4×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C2×M64

222 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, 89752);