Finite Group Databasebeta

C2×#14529246 #17036142

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

Aliases

direct productC2×#14529246

Splittings

FittingC2×C17×#343 ⋊ C2
SylowC17 ⋊ C2×#1900

Subgroups

subgroupG/H
centerC23C22⋊C4×D17
commutatorC23×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#343C2
socleC23×C17C2×C22⋊C4
prime radicalC22×#10587581C2
cosocleC22×C4×C17C24
hypercenterC2×#343D17
hypocenterC17C2×#1900
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

2198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 171386);