Finite Group Databasebeta

Q8×#10587528 #17982813

order4352
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C22

Aliases

direct productQ8×#10587528

Splittings

SylowC17 ⋊ Q8×C32

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×#3633
commutatorC2×C17C22×C32
FittingC4×Q8×C17C8
socle, prime radicalC22×C17C22×C16
cosocleC2×#63216C23
hypercenterC4×Q8#3633
hypocenterC17Q8×C32
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C4×Q8

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118057);