Finite Group Databasebeta

C2×#20244408 #26243168

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

Aliases

direct productC2×#20244408

Splittings

FittingC2×C47×#536 ⋊ C2
SylowC47 ⋊ C2×#2003

Subgroups

subgroupG/H
centerC23#13093993
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#536C2
socleC23×C47#120
prime radicalC22×#13094049C2
hypercenterC2×#536D47
hypocenterC47C2×#2003
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#536

2126 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 196458);