Finite Group Databasebeta

C2×#20244302 #26220277

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20244302

Splittings

SylowC47 ⋊ C2×#1979

Subgroups

subgroupG/H
centerC23#13093996
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#419C2
socleC23×C47#121
prime radicalC24×C47#41
cosocleC22×C4×C47C24
hypercenterC2×#419D47
hypocenterC47C2×#1979
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

1438 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, 173567);