Finite Group Databasebeta

C2×SD16×Dic34 #17914744

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

Aliases

direct productC2×SD16×Dic34

Splittings

SylowC17 ⋊ C2×Q8×SD16

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C4×SD16×C17C2
socleC23×C17C22×D4
prime radicalC22×D4×C17C23
hypercenterC2×C4×SD16D17
hypocenterC17C2×Q8×SD16
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

2058 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, 1049988);