Finite Group Databasebeta

C2×#20244057 #26218859

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20244057

Splittings

FittingC2×C4×M16×C47 ⋊ C2
SylowC47 ⋊ C2×#1932

Subgroups

subgroupG/H
centerC2×C4#13093998
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C4×M16×C47C2
socleC22×C47#388
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×C4×M16D47
hypocenterC47C2×#1932
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×M16

1046 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 172149);