Finite Group Databasebeta

M16×#10625329 #26181988

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productM16×#10625329

Splittings

SylowC47 ⋊ M162

Subgroups

subgroupG/H
center, FrattiniC42C23×D47
commutator, socleC22×C47C22×C42
FittingC2×C4×M16×C47C2
prime radicalC24×C47C42
cosocleC42×C47C24
hypercenterC2×C4×M16D47
hypocenterC47M162
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C42 ◁ C2×C4×M16

900 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 135278);