Finite Group Databasebeta

C2×#20245515 #26370844

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

Aliases

direct productC2×#20245515

Splittings

FittingC22×SD32×C47 ⋊ C2
SylowC47 ⋊ C2×#2223

Subgroups

subgroupG/H
centerC22#15689356
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC22×SD32×C47C2
socleC22×C47#466
prime radicalC2×#15689390C2
hypercenterC22×SD32D47
hypocenterC47C2×#2223
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

658 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 324134);