Finite Group Databasebeta

C2×#20241527 #26136478

order12032
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20241527

Splittings

FittingC2×C47×M64 ⋊ C2
SylowC47 ⋊ C2×#1400

Subgroups

subgroupG/H
centerC2×C8(C2×D47)⋊C4
commutatorC22×C47C22×C16
FrattiniC2×C16C22×D47
FittingC2×C47×M64C2
socleC22×C47C22⋊C16
prime radicalC23×D47C16
cosocleC2×C16×C47C23
hypercenterC2×M64D47
hypocenterC47C2×#1400
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ C2×M64

306 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 89768);