Finite Group Databasebeta

C22×#11762783 #17897789

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×#11762783

Splittings

SylowC17 ⋊ C22×#410

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
Fitting, prime radicalC23×#41×C17C2
socleC23×C17C2×C22⋊C4
cosocleC23×C17C25
hypercenterC23×#41D17
hypocenterC17C22×#410
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×#41

5278 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, 1033033);