Finite Group Databasebeta

C2×#20241270 #26106326

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241270

Splittings

SylowC47 ⋊ C2×#1295

Subgroups

subgroupG/H
centerC24(C2×D47)⋊C4
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC22×#97×C47C2
socle, prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC22×#97D47
hypocenterC47C2×#1295
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#97

830 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 59616);