Finite Group Databasebeta

C2×#20246725 #26384971

order12032
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#20246725

Splittings

FittingC2×C47×#381 ⋊ C2
SylowC47 ⋊ C2×#2406

Subgroups

subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#381C2
socleC24×C47C24
prime radicalC23×#10625350C2
hypercenterC2×#381D47
hypocenterC47C2×#2406
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#381

5718 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 338261);