Finite Group Databasebeta

C22×#11762532 #17000109

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11762532

Splittings

FittingC22×C17×C22⋊C8 ⋊ C2
SylowC17 ⋊ C22×#323

Subgroups

subgroupG/H
centerC24#63227
commutatorC22×C17C23×C8
FrattiniC22×C4C23×D17
FittingC22×C17×C22⋊C8C2
socleC24×C17C22⋊C4
prime radicalC25×D17C4
cosocleC22×C4×C17C24
hypercenterC22×C22⋊C8D17
hypocenterC17C22×#323
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

2878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135353);