Finite Group Databasebeta

Q8×#10587502 #16955810

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productQ8×#10587502

Splittings

SylowC17 ⋊ Q8×#95

Subgroups

subgroupG/H
center, FrattiniC24C23×D17
commutatorC22×C17C22×C42
FittingC22×C4×Q8×C17C2
socle, prime radical, cosocleC24×C17C24
hypercenterC22×C4×Q8D17
hypocenterC17Q8×#95
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×Q8

2434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 91054);