Finite Group Databasebeta

C2×#20244500 #26243468

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

Aliases

direct productC2×#20244500

Splittings

FittingC23×SD16×C47 ⋊ C2
SylowC47 ⋊ C2×#2019

Subgroups

subgroupG/H
centerC23#13093995
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC23×SD16×C47C2
socleC23×C47#121
prime radicalC22×#13094050C2
hypercenterC23×SD16D47
hypocenterC47C2×#2019
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×SD16

2030 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 196758);