Finite Group Databasebeta

C22×#11762587 #17186978

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11762587

Splittings

SylowC17 ⋊ C22×#347

Subgroups

subgroupG/H
centerC22×C4C4×Dic17
commutatorC4×C17C22×C42
FrattiniC2×C8C23×D17
FittingC22×C17×#97C2
socleC23×C17#97
prime radicalC24×C17M16
cosocleC2×C8×C17C24
hypercenterC22×#97D17
hypocenterC17C22×#347
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×#97

782 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, 322222);