Finite Group Databasebeta

Q16×#63252 #17915794

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

Aliases

direct productQ16×#63252

Splittings

FittingC2×C4×Q16×C17 ⋊ C2
SylowC17 ⋊ Q16×#41

Subgroups

subgroupG/H
centerC2×C4C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C4×Q16×C17C2
socleC22×C17C23×D4
prime radicalC2×#63252D4
hypercenterC2×C4×Q16D17
hypocenterC17Q16×#41
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q16

1826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1051038);