Finite Group Databasebeta

C16×#10625350 #26369795

order12032
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC16×#10625350

Splittings

FittingC2×C4×C16×C47 ⋊ C2
SylowC47 ⋊ C16×#41

Subgroups

subgroupG/H
centerC4×C16C2×D47
commutatorC2×C47C23×C16
FrattiniC2×C8C23×D47
FittingC2×C4×C16×C47C2
socleC22×C47C23×C8
prime radicalC2×#10625350C8
cosocleC2×C8×C47C24
hypercenterC2×C4×C16D47
hypocenterC47C16×#41
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C16 ◁ C2×C4×C16

602 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323085);