Finite Group Databasebeta

D8×#10625329 #26187701

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD8×#10625329

Splittings

SylowC47 ⋊ M16×D8

Subgroups

subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C4×D8×C47C2
socleC22×C47C2×C4×D4
prime radicalC22×D8×C47C4
cosocleC42×C47C24
hypercenterC2×C4×D8D47
hypocenterC47M16×D8
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D8

794 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, 140991);