Finite Group Databasebeta

C2×D17×#421 #17897914

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×D17×#421

Splittings

FittingC2×C17×#421 ⋊ C2
SylowC17 ⋊ C22×#421

Subgroups

subgroupG/H
centerC2×C4C2×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#421C2
socleC22×C17C22×C22⋊C4
prime radicalC22×#41×D17C2
cosocleC2×C4×C17C25
hypercenterC2×#421D17
hypocenterC17C22×#421
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

5198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033158);