Finite Group Databasebeta

C2×#20245200 #26369400

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

Aliases

direct productC2×#20245200

Splittings

SylowC47 ⋊ C2×#2165

Subgroups

subgroupG/H
centerC2×C4#13093983
commutatorC2×C4×C47C23×C4
FrattiniC2×C8C23×D47
FittingC2×C4×M16×C47C2
socleC22×C47#432
prime radicalC24×C47M16
cosocleC2×C8×C47C24
hypercenterC2×C4×M16D47
hypocenterC47C2×#2165
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ C2×C4×M16

570 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322690);