Finite Group Databasebeta

C2×#20244444 #26243274

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20244444

Splittings

FittingC2×C47×#344 ⋊ C2
SylowC47 ⋊ C2×#2008

Subgroups

subgroupG/H
centerC22#15689033
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#344C2
socleC22×C47#392
hypercenterC2×#344D47
hypocenterC47C2×#2008
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

2118 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, 196564);