Finite Group Databasebeta

C2×#14545779 #17981058

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×#14545779

Splittings

SylowC17 ⋊ C2×#3573

Subgroups

subgroupG/H
centerC22C24×#595
commutatorC2×C17C25×C4
FrattiniC2C25×#595
FittingC2×C17×H(5,𝔽2)C4
socleC22×C17C24×C4
prime radicalC2×#11763644C2
cosocleDic17C26
hypercenterC2×H(5,𝔽2)#595
hypocenterC17C2×#3573
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×H(5,𝔽2)

10858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1116302);