Finite Group Databasebeta

C22×#11763318 #17940979

order4352
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×#11763318

Splittings

FittingC22×C4×D4×C17 ⋊ C2
SylowC17 ⋊ C22×#525

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC22×C4×D4×C17C2
socleC24×C17C24
hypercenterC22×C4×D4D17
hypocenterC17C22×#525
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076223);