Finite Group Databasebeta

C22×#11763773 #17979409

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×#11763773

Splittings

SylowC17 ⋊ C22×#405

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC2×C17C23×C42
FrattiniC22C24×#595
FittingC22×C22⋊C4×C17C4
socleC24×C17C22×C4
prime radicalC25×C17C2×C4
cosocleC2×Dic17C25
hypercenterC22×C22⋊C4#595
hypocenterC17C22×#405
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C22⋊C4

3518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114653);