Finite Group Databasebeta

C2×#20242788 #26198542

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20242788

Splittings

FittingC2×C47×#335 ⋊ C2
SylowC47 ⋊ C2×#1675

Subgroups

subgroupG/H
centerC23#13093999
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC2×C47×#335C2
socleC23×C47#121
prime radicalC22×D188D4
hypercenterC2×#335D47
hypocenterC47C2×#1675
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

726 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1346 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 151832);