Finite Group Databasebeta

C2×#20245344 #26370200

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20245344

Splittings

FittingC22×D16×C47 ⋊ C2
SylowC47 ⋊ C2×#2192

Subgroups

subgroupG/H
centerC22#15689255
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC22×D16×C47C2
socleC22×C47#447
hypercenterC22×D16D47
hypocenterC47C2×#2192
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

1150 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1058 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323490);