Finite Group Databasebeta

Q8×#88158 #16743388

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

Aliases

direct productQ8×#88158

Splittings

FittingC2×C8×Q8×C13 ⋊ C2
SylowC13 ⋊ Q8×#135

Subgroups

subgroupG/H
centerC2×C4C22×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C8×Q8×C13C2
socleC22×C13C23×D4
prime radicalC2×#88158C22
hypercenterC2×C8×Q8D13
hypocenterC13Q8×#135
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ C2×C8×Q8

1786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1050037);