Finite Group Databasebeta

C2×#20248123 #26385574

order12032
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20248123

Splittings

SylowC47 ⋊ C2×#2524

Subgroups

subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#398C2
socle, prime radicalC24×C47C24
hypercenterC2×#398D47
hypocenterC47C2×#2524
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#398

1878 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 338864);