Finite Group Databasebeta

Q8×#88162 #16743499

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#88162

Splittings

FittingQ8×C13×M16 ⋊ C2
SylowC13 ⋊ Q8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22C23×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingQ8×C13×M16C2
socleC22×C13C23×D4
prime radicalC2×#88162C22
hypercenterQ8×M16D13
hypocenterC13Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×M16

2010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1050148);