Finite Group Databasebeta

C2×#20241610 #26137367

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C210

Aliases

direct productC2×#20241610

Splittings

SylowC47 ⋊ C2×C22⋊#95

Subgroups

subgroupG/H
centerC25C22×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC23×C22⋊C4×C47C2
socleC25×C47C23
prime radicalC26×C47C22
cosocleC24×C47C24
hypercenterC23×C22⋊C4D47
hypocenterC47C2×C22⋊#95
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C25 ◁ C23×C22⋊C4

7630 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 90657);