Finite Group Databasebeta

C2×#14545903 #17982848

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14545903

Splittings

FittingC2×#41×C17 ⋊ C8
SylowC17 ⋊ C2×#1477

Subgroups

subgroupG/H
centerC22C2×C22⋊#3633
commutatorC4×C17C23×C8
FrattiniC4C23×#3633
FittingC2×#41×C17C8
socleC22×C17C2×C22⋊C8
prime radicalC2×#41×D17C4
cosocleC4×#595C24
hypercenterC2×#41#3633
hypocenterC17C2×#1477
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

1370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118092);