Finite Group Databasebeta

Q8×M16×D17 #17898707

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productQ8×M16×D17

Splittings

FittingQ8×M16×C17 ⋊ C2
SylowC17 ⋊ C2×Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D17
commutator, socleC22×C17C24×C4
FittingQ8×M16×C17C2
prime radicalC23×D17C22×C4
cosocleC2×C4×C17C25
hypercenterQ8×M16D17
hypocenterC17C2×Q8×M16
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ Q8×M16

2154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033951);