Finite Group Databasebeta

C2×#20245222 #26369503

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20245222

Splittings

FittingC2×C47×#350 ⋊ C2
SylowC47 ⋊ C2×#2170

Subgroups

subgroupG/H
centerC2×C8D4×D47
commutatorC4×C47C23×C8
FrattiniC2×C8C23×D47
FittingC2×C47×#350C2
socleC22×C47C8×D4
prime radicalC2×#13094044C4
cosocleC2×C8×C47C24
hypercenterC2×#350D47
hypocenterC47C2×#2170
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

662 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322793);