Finite Group Databasebeta

Q8×#13093981 #26375702

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productQ8×#13093981

Splittings

FittingC42×Q8×C47 ⋊ C2
SylowC47 ⋊ Q8×#117

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC42×Q8×C47C2
socle, cosocleC23×C47C25
prime radicalC23×D47C24
hypercenterC42×Q8D47
hypocenterC47Q8×#117
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C42×Q8

2434 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328992);