Finite Group Databasebeta

C2×#20241483 #26131170

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241483

Splittings

SylowC47 ⋊ C2×#1382

Subgroups

subgroupG/H
centerC22×C4#10625334
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC2×C47×#427C2
socleC23×C47#102
prime radicalC24×C47SD16
cosocleC22×C8×C47C23
hypercenterC2×#427D47
hypocenterC47C2×#1382
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

590 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84460);