Finite Group Databasebeta

C22×#11763795 #17979485

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11763795

Splittings

SylowC17 ⋊ C22×#413

Subgroups

subgroupG/H
centerC22×C4C22⋊#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC24×C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×#63252C2
cosocleC2×Dic17C25
hypercenterC24×C4#595
hypocenterC17C22×#413
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C24×C4

5118 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, 1114729);