Finite Group Databasebeta

C2×#20241475 #26131144

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241475

Splittings

SylowC47 ⋊ C2×#1378

Subgroups

subgroupG/H
centerC2×C8(C2×D47)⋊C4
commutatorC22×C47C2×C4×C8
FrattiniC22×C8C22×D47
FittingC22×M32×C47C2
socleC22×C47#336
prime radicalC24×C47C2×C8
cosocleC22×C8×C47C23
hypercenterC22×M32D47
hypocenterC47C2×#1378
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×M32

586 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84434);