Finite Group Databasebeta

C2×#20242406 #26188397

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

Aliases

direct productC2×#20242406

Splittings

FittingC2×C47×#481 ⋊ C2
SylowC47 ⋊ C2×#1613

Subgroups

subgroupG/H
centerC23#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#481C2
socleC23×C47#120
prime radicalC2×#15689681C2
hypercenterC2×#481D47
hypocenterC47C2×#1613
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

1524 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

920 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 141687);