Finite Group Databasebeta

C2×#14545930 #17982902

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14545930

Splittings

FittingC22×D4×C17 ⋊ C8
SylowC17 ⋊ C2×#1869

Subgroups

subgroupG/H
centerC23C22×#3633
commutatorC22×C17C23×C8
FrattiniC22C23×#3633
FittingC22×D4×C17C8
socleC23×C17C22×C8
prime radicalC22×D4×D17C4
cosocleC22×#595C24
hypercenterC22×D4#3633
hypocenterC17C2×#1869
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×D4

2438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118146);