Finite Group Databasebeta

C2×D17×#362 #17187277

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D17×#362

Splittings

FittingC2×C17×#362 ⋊ C2
SylowC17 ⋊ C22×#362

Subgroups

subgroupG/H
centerC22#102×D17
commutatorC8×C17C23×C4
FrattiniC2×C8C23×D17
FittingC2×C17×#362C2
socleC22×C17C2×#102
prime radicalC23×D17SD16
cosocleC2×C8×C17C24
hypercenterC2×#362D17
hypocenterC17C22×#362
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

1134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322521);