Finite Group Databasebeta

C2×#20243142 #26213780

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC2×#20243142

Splittings

SylowC47 ⋊ C2×#1747

Subgroups

subgroupG/H
centerC2×C4C42×D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC2×C47×H(3,ℤ/4)C2
socleC22×C47#376
prime radicalC24×C47#41
cosocleC22×C4×C47C24
hypercenterC2×H(3,ℤ/4)D47
hypocenterC47C2×#1747
LCSG ▷ C4×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

930 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167070);