Finite Group Databasebeta

C2×#20243880 #26218166

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20243880

Splittings

FittingC2×C47×#419 ⋊ C2
SylowC47 ⋊ C2×#1905

Subgroups

subgroupG/H
centerC22#15689000
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#419C2
socleC22×C47#386
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×#419D47
hypocenterC47C2×#1905
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#419

1678 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 171456);