Finite Group Databasebeta

C2×D17×#368 #17187374

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×D17×#368

Splittings

FittingC2×C17×#368 ⋊ C2
SylowC17 ⋊ C22×#368

Subgroups

subgroupG/H
centerC2×C4D8×D17
commutatorC8×C17C23×C4
FrattiniC2×C8C23×D17
FittingC2×C17×#368C2
socleC22×C17C2×#107
prime radicalC23×D17Q16
cosocleC2×C8×C17C24
hypercenterC2×#368D17
hypocenterC17C22×#368
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#368

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 322618);