Finite Group Databasebeta

C22×#11762590 #17187009

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11762590

Splittings

FittingC22×C17×M32 ⋊ C2
SylowC17 ⋊ C22×#349

Subgroups

subgroupG/H
centerC22×C4#63227
commutatorC22×C17C23×C8
FrattiniC2×C8C23×D17
FittingC22×C17×M32C2
socleC23×C17C22⋊C8
prime radicalC24×D17C8
cosocleC2×C8×C17C24
hypercenterC22×M32D17
hypocenterC17C22×#349
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×M32

1262 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, 322253);