Finite Group Databasebeta

Q8×#14268646 #28404151

order14464
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#14268646

Splittings

FittingD4×Q8×C113 ⋊ C2
SylowC113 ⋊ Q8×#41

Subgroups

subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
FittingD4×Q8×C113C2
prime radicalC2×#14268646C22
hypercenterD4×Q8D113
hypocenterC113Q8×#41
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ D4×Q8

1068 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 18087);