Finite Group Databasebeta

M16×#10625336 #26187718

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×#10625336

Splittings

FittingQ8×M16×C47 ⋊ C2
SylowC47 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingQ8×M16×C47C2
socleC22×C47C2×C4×D4
prime radicalC22×D188C2×C4
cosocleC42×C47C24
hypercenterQ8×M16D47
hypocenterC47M16×SD16
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ Q8×M16

716 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 141008);