Finite Group Databasebeta

C2×#20241676 #26181876

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20241676

Splittings

FittingC2×C47×#322 ⋊ C2
SylowC47 ⋊ C2×#1451

Subgroups

subgroupG/H
centerC2×C42C22×D47
commutatorC22×C47C22×C42
FrattiniC42C23×D47
FittingC2×C47×#322C2
socleC23×C47C2×C42
prime radicalC23×D47C42
cosocleC42×C47C24
hypercenterC2×#322D47
hypocenterC47C2×#1451
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C2×#322

966 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 135166);