Finite Group Databasebeta

C2×#20241528 #26136479

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

Aliases

direct productC2×#20241528

Splittings

SylowC47 ⋊ C2×#1400

Subgroups

subgroupG/H
centerC2×C8C22⋊Dic47
commutatorC22×C47C22×C16
FrattiniC2×C16C22×D47
FittingC22×M32×C47C2
socleC22×C47C22⋊C16
prime radicalC24×C47C16
cosocleC2×C16×C47C23
hypercenterC22×M32D47
hypocenterC47C2×#1400
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ C22×M32

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, 89769);