Finite Group Databasebeta

Q8×#10587636 #17914787

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

Aliases

direct productQ8×#10587636

Splittings

FittingQ8×#41×C17 ⋊ C2
SylowC17 ⋊ Q8×#135

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingQ8×#41×C17C2
socleC22×C17C23×D4
prime radicalC2×#10587636C22
hypercenterQ8×#41D17
hypocenterC17Q8×#135
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ Q8×#41

1786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1050031);