Finite Group Databasebeta

C22×#11763689 #17968218

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11763689

Splittings

SylowC17 ⋊ C22×#343

Subgroups

subgroupG/H
centerC24C22⋊#595
commutatorC22×C17C22×C42
FrattiniC23C23×#595
FittingC24×C4×C17C4
socleC24×C17C22⋊C4
prime radicalC25×C17C2×C4
cosocleC22×Dic17C24
hypercenterC24×C4#595
hypocenterC17C22×#343
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C25 ◁ C24×C4

2494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 1103462);