Finite Group Databasebeta

C2×#20241492 #26131190

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

Aliases

direct productC2×#20241492

Splittings

SylowC47 ⋊ C2×#1385

Subgroups

subgroupG/H
centerC2×C4#13093956
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC22×M32×C47C2
socleC22×C47#340
prime radicalC24×C47Q16
cosocleC22×C8×C47C23
hypercenterC22×M32D47
hypocenterC47C2×#1385
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

554 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84480);