Finite Group Databasebeta

M16×C47⋊C16 #26125290

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

Aliases

direct productM16×C47⋊C16

Splittings

SylowC47 ⋊ C16×M16

Subgroups

subgroupG/H
center, FrattiniC4×C8C22×D47
commutatorC2×C47C2×C4×C16
FittingC8×M16×C47C2
socleC22×C47C2×C4×C8
prime radicalC23×C47C4×C8
cosocleC4×C8×C47C23
hypercenterC8×M16D47
hypocenterC47C16×M16
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C8 ◁ C8×M16

306 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 78580);