Finite Group Databasebeta

C2×#14538521 #17901738

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14538521

Splittings

FittingC2×C17×#568 ⋊ C2
SylowC17 ⋊ C2×#3069

Subgroups

subgroupG/H
centerC22C2×#10587616
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#568C2
socleC22×C17C2×#121
prime radicalC2×#11763607C2
hypercenterC2×#568D17
hypocenterC17C2×#3069
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#568

2618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1036982);