Finite Group Databasebeta

C2×#20245276 #26369708

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20245276

Splittings

SylowC47 ⋊ C2×#2180

Subgroups

subgroupG/H
centerC22#15689232
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC2×C47×#360C2
socleC22×C47#442
prime radicalC2×#135×C47C22
cosocleC2×C8×C47C24
hypercenterC2×#360D47
hypocenterC47C2×#2180
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

646 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322998);