Finite Group Databasebeta

C22×#11763277 #17940897

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×#11763277

Splittings

FittingC22×C17×#117 ⋊ C2
SylowC17 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC2×C17C25×C4
FrattiniC22C25×D17
FittingC22×C17×#117C2
socleC24×C17C24
prime radicalC23×#63252C2
cosocleC22×C17C26
hypercenterC22×#117D17
hypocenterC17C22×C4×#41
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×#117

12878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076141);