Finite Group Databasebeta

C2×#20244581 #26243731

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

Aliases

direct productC2×#20244581

Splittings

SylowC47 ⋊ C2×#2035

Subgroups

subgroupG/H
centerC24C2×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×C22⋊Q8×C47C2
socleC24×C47C2×D4
prime radicalC25×C47D4
hypercenterC22×C22⋊Q8D47
hypocenterC47C2×#2035
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊Q8

1662 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, 197021);