Finite Group Databasebeta

C2×#14529167 #17035864

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14529167

Splittings

FittingC2×C17×#568 ⋊ C2
SylowC17 ⋊ C2×#1884

Subgroups

subgroupG/H
centerC2×C4#10587639
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#568C2
socleC22×C17#386
prime radicalC2×#11763355C2
cosocleC22×C4×C17C24
hypercenterC2×#568D17
hypocenterC17C2×#1884
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#568

1794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 171108);