Finite Group Databasebeta

C2×D17×#407 #17897752

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

Aliases

direct productC2×D17×#407

Splittings

FittingC2×C17×#407 ⋊ C2
SylowC17 ⋊ C22×#407

Subgroups

subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#407C2
socleC23×C17C23×C4
prime radicalC25×D17C4
cosocleC2×C4×C17C25
hypercenterC2×#407D17
hypocenterC17C22×#407
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#407

7214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1032996);