Finite Group Databasebeta

C2×#20244346 #26220788

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20244346

Splittings

SylowC47 ⋊ C2×#1989

Subgroups

subgroupG/H
centerC24C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#125×C47C2
socle, prime radicalC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenterC22×#125D47
hypocenterC47C2×#1989
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#125

1294 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, 174078);