Finite Group Databasebeta

C2×#20243906 #26218212

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

Aliases

direct productC2×#20243906

Splittings

FittingC22×#103×C47 ⋊ C2
SylowC47 ⋊ C2×#1908

Subgroups

subgroupG/H
centerC23#13093995
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#103×C47C2
socleC23×C47#121
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC22×#103D47
hypocenterC47C2×#1908
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

1698 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 171502);