Finite Group Databasebeta

SD16×C22⋊Dic47 #26232111

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productSD16×C22⋊Dic47

Splittings

SylowC47 ⋊ C22⋊C4×SD16

Subgroups

subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC23×SD16×C47C2
socleC23×C47C22×D4
prime radicalC23×D4×C47C22
cosocleC22×C4×C47C24
hypercenterC23×SD16D47
hypocenterC47C22⋊C4×SD16
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×SD16

1614 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1358 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 185401);