Finite Group Databasebeta

C16×#10625329 #26125292

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4

Aliases

direct productC16×#10625329

Splittings

SylowC47 ⋊ C16×M16

Subgroups

subgroupG/H
centerC4×C16C2×D47
commutatorC2×C47C2×C4×C16
FrattiniC4×C8C22×D47
FittingC2×C4×C16×C47C2
socleC22×C47C2×C4×C8
prime radicalC23×C47C4×C8
cosocleC4×C8×C47C23
hypercenterC2×C4×C16D47
hypocenterC47C16×M16
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C16 ◁ C2×C4×C16

306 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, 78582);