Finite Group Databasebeta

C2×#20241484 #26131171

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

Aliases

direct productC2×#20241484

Splittings

SylowC47 ⋊ C2×#1382

Subgroups

subgroupG/H
centerC22×C4D376
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC23×C16×C47C2
socleC23×C47#102
prime radicalC24×C47SD16
cosocleC22×C8×C47C23
hypercenterC23×C16D47
hypocenterC47C2×#1382
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C23×C16

590 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84461);