Finite Group Databasebeta

C2×#14545415 #17979519

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

Aliases

direct productC2×#14545415

Splittings

FittingC2×C17×2−1+4 ⋊ C4
SylowC17 ⋊ C2×#2901

Subgroups

subgroupG/H
centerC22C22×C22⋊#595
commutatorC4×C17C24×C4
FrattiniC4C24×#595
FittingC2×C17×2−1+4C4
socleC22×C17C22×C22⋊C4
prime radicalC2×#11763646C2
cosocleC4×D17C25
hypercenterC2×2−1+4#595
hypocenterC17C2×#2901
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×2−1+4

4946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114763);