Finite Group Databasebeta

C2×#20245749 #26374497

order12032
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#20245749

Splittings

SylowC47 ⋊ C2×#2275

Subgroups

subgroupG/H
centerC24C23×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC22×C4×D4×C47C2
socleC24×C47C24
prime radicalC23×D4×C47C22
cosocleC23×C47C25
hypercenterC22×C4×D4D47
hypocenterC47C2×#2275
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4×D4

4694 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327787);