Finite Group Databasebeta

C2×#20241605 #26137327

order12032
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20241605

Splittings

SylowC47 ⋊ C2×Q128

Subgroups

subgroupG/H
centerC22#15688958
commutator, cosocleC32×C47C23
FrattiniC32C22×D47
FittingC2×C47×Q64C2
socle, prime radicalC22×C47D32
hypercenterC2×Q64D47
hypocenterC47C2×Q128
LCSG ▷ C32×C47 ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×Q64

126 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

944 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 90617);