Finite Group Databasebeta

C2×#20245410 #26370437

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20245410

Splittings

FittingC2×C47×#356 ⋊ C2
SylowC47 ⋊ C2×#2203

Subgroups

subgroupG/H
centerC22#15689311
commutator, cosocleC2×Q8×C47C24
FrattiniC2×Q8C23×D47
FittingC2×C47×#356C2
socleC22×C47B(4,𝔽2)
prime radicalC2×#15689298C2
hypercenterC2×#356D47
hypocenterC47C2×#2203
LCSG ▷ C2×Q8×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

1092 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

632 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323727);