Finite Group Databasebeta

C2×#20243606 #26217117

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20243606

Splittings

FittingC2×C47×#430 ⋊ C2
SylowC47 ⋊ C2×#1858

Subgroups

subgroupG/H
centerC2×C4#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#430C2
socleC22×C47#385
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×#430D47
hypocenterC47C2×#1858
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

1310 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 170407);