Finite Group Databasebeta

C2×#20244653 #26244073

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20244653

Splittings

SylowC47 ⋊ C2×#2047

Subgroups

subgroupG/H
centerC23#13093995
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC23×Q16×C47C2
socleC23×C47#121
prime radicalC24×C47#41
hypercenterC23×Q16D47
hypocenterC47C2×#2047
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

1330 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, 197363);