Finite Group Databasebeta

C22×#11763676 #17968166

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC22×#11763676

Splittings

FittingC22×C42×C17 ⋊ C4
SylowC17 ⋊ C22×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC22×C4C4×#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC22×C42×C17C4
socleC23×C17#95
prime radicalC24×D17D4
cosocleC2×C4×D17C24
hypercenterC22×C42#595
hypocenterC17C22×H(3,ℤ/4)
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42

2270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103410);