Finite Group Databasebeta

C8×D4×Dic47 #26214591

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC8×D4×Dic47

Splittings

SylowC47 ⋊ C4×C8×D4

Subgroups

subgroupG/H
centerC22×C8C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC2×C8×D4×C47C2
socleC23×C47C23×C4
prime radicalC22×D4×C47C2×C4
cosocleC22×C4×C47C24
hypercenterC2×C8×D4D47
hypocenterC47C4×C8×D4
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C2×C8×D4

1422 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, 167881);