Finite Group Databasebeta

Q8×#92495 #16859292

order3968
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#92495

Splittings

FittingC2×C4×Q8×C31 ⋊ C2
SylowC31 ⋊ Q8×#41

Subgroups

subgroupG/H
centerC2×C4C23×D31
commutator, socle, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC2×C4×Q8×C31C2
prime radicalC2×#92495C22
hypercenterC2×C4×Q8D31
hypocenterC31Q8×#41
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

1068 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 18091);