Finite Group Databasebeta

C2×#14537637 #17898453

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14537637

Splittings

FittingC2×C17×#405 ⋊ C2
SylowC17 ⋊ C2×#2948

Subgroups

subgroupG/H
centerC23C22×D68
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#405C2
socleC23×C17C22×D4
prime radicalC23×D136C2
cosocleC2×C4×C17C25
hypercenterC2×#405D17
hypocenterC17C2×#2948
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033697);