Finite Group Databasebeta

C2×#14537702 #17898646

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

Aliases

direct productC2×#14537702

Splittings

FittingC2×C17×#405 ⋊ C2
SylowC17 ⋊ C2×#2957

Subgroups

subgroupG/H
centerC2×C4C22×D68
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#405C2
socleC22×C17C2×C4×D4
prime radicalC22×#10587590C2
cosocleC2×C4×C17C25
hypercenterC2×#405D17
hypocenterC17C2×#2957
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ C2×#405

2642 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, 1033890);