Finite Group Databasebeta

C2×#20244857 #26245225

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20244857

Splittings

SylowC47 ⋊ C2×#2082

Subgroups

subgroupG/H
centerC22#15689052
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×H(3,ℤ/4)C2
socleC22×C47#397
prime radicalC24×C47#41
hypercenterC2×H(3,ℤ/4)D47
hypocenterC47C2×#2082
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

878 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1058 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 198515);