Finite Group Databasebeta

C2×#20245040 #26369013

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20245040

Splittings

FittingC2×C47×#352 ⋊ C2
SylowC47 ⋊ C2×#2123

Subgroups

subgroupG/H
centerC22#99×D47
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
FittingC2×C47×#352C2
socleC22×C47C2×#99
prime radicalC22×#10625352C22
cosocleC2×D4×C47C24
hypercenterC2×#352D47
hypocenterC47C2×#2123
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

1214 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

644 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322303);