Finite Group Databasebeta

Q8×#10587493 #17053214

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productQ8×#10587493

Splittings

SylowC17 ⋊ Q8×#108

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingQ8×M16×C17C2
socleC22×C17C22×C4⋊C4
prime radicalC23×C17C22×Q8
cosocleC22×C4×C17C24
hypercenterQ8×M16D17
hypocenterC17Q8×#108
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ Q8×M16

658 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, 188458);