Finite Group Databasebeta

C2×#20241875 #26183367

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

Aliases

direct productC2×#20241875

Splittings

FittingC2×C47×#431 ⋊ C2
SylowC47 ⋊ C2×#1500

Subgroups

subgroupG/H
centerC22×C4(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#431C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenterC2×#431D47
hypocenterC47C2×#1500
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

1182 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, 136657);