Finite Group Databasebeta

C2×#342×D47 #26213704

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productC2×#342×D47

Splittings

FittingC2×C47×#342 ⋊ C2
SylowC47 ⋊ C22×#342

Subgroups

subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC2×C47×#342C2
socleC23×C47C2×C22⋊C4
prime radicalC25×D47C22
cosocleC24×C47C24
hypercenterC2×#342D47
hypocenterC47C22×#342
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

4334 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 166994);