Finite Group Databasebeta

Q8×#13093989 #26376280

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#13093989

Splittings

SylowC47 ⋊ C4×Q82

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingQ8×C4⋊C4×C47C2
socle, prime radical, cosocleC23×C47C25
hypercenterQ8×C4⋊C4D47
hypocenterC47C4×Q82
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

2324 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, 329570);