Finite Group Databasebeta

C2×#14545344 #17979410

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#14545344

Splittings

SylowC17 ⋊ C22×#405

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC2×C17C23×C42
FrattiniC22C24×#595
FittingC2×C17×#117C4
socleC23×C17C23×C4
prime radicalC24×D17C2×C4
cosocleC2×Dic17C25
hypercenterC2×#117#595
hypocenterC17C22×#405
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#117

3518 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, 1114654);