Finite Group Databasebeta

C2×#20241208 #26104208

order12032
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20241208

Splittings

FittingC2×C47×#336 ⋊ C2
SylowC47 ⋊ C2×#1270

Subgroups

subgroupG/H
centerC24(C2×D47)⋊C4
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC2×C47×#336C2
socleC24×C47C22⋊C4
prime radicalC23×D188C4
cosocleC2×C42×C47C23
hypercenterC2×#336D47
hypocenterC47C2×#1270
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

994 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, 57498);