Finite Group Databasebeta

C22×#11763050 #17901422

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11763050

Splittings

SylowC17 ⋊ C22×#467

Subgroups

subgroupG/H
centerC24C2×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC24×C8×C17C2
socleC24×C17C2×D4
prime radicalC25×C17D4
hypercenterC24×C8D17
hypocenterC17C22×#467
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C24×C4 ◁ C24×C8

3006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1036666);