Finite Group Databasebeta

C22×#11762626 #17187280

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11762626

Splittings

SylowC17 ⋊ C22×#362

Subgroups

subgroupG/H
centerC23#10587492
commutatorC8×C17C23×C4
FrattiniC2×C8C23×D17
FittingC22×C17×M32C2
socleC23×C17#102
prime radicalC24×C17SD16
cosocleC2×C8×C17C24
hypercenterC22×M32D17
hypocenterC17C22×#362
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

1134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322524);