Finite Group Databasebeta

C2×Q8×D659 #35231358

order21088
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×D659

Splittings

FittingC2×Q8×C659 ⋊ C2
SylowC659 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC22C22×D659
commutator, cosocleC2×C659C24
FrattiniC2C23×D659
FittingC2×Q8×C659C2
socleC22×C659C23
prime radicalC22×D659C22
hypercenterC2×Q8D659
hypocenterC659C22×Q8
LCSG ▷ C2×C659 ▷ C659
UCSC1 ◁ C22 ◁ C2×Q8

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10544

Conjugacy classes & character table

3310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21088, 185);