Finite Group Databasebeta

Q8×C22⋊C4×D47 #26375463

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productQ8×C22⋊C4×D47

Splittings

FittingQ8×C22⋊C4×C47 ⋊ C2
SylowC47 ⋊ C2×Q8×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingQ8×C22⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC24×D47C23
hypercenterQ8×C22⋊C4D47
hypocenterC47C2×Q8×C22⋊C4
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

5414 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328753);