Finite Group Databasebeta

Q8×#10587605 #17914794

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#10587605

Splittings

FittingQ8×Q16×C17 ⋊ C2
SylowC17 ⋊ Q8×#135

Subgroups

subgroupG/H
centerC22C22×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingQ8×Q16×C17C2
socleC22×C17C23×D4
prime radicalC2×#10587605C22
hypercenterQ8×Q16D17
hypocenterC17Q8×#135
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q8×Q16

1786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1050038);