Finite Group Databasebeta

C22×#11762535 #17000113

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11762535

Splittings

SylowC17 ⋊ C22×#324

Subgroups

subgroupG/H
centerC24C22⋊Dic17
commutatorC22×C17C23×C8
FrattiniC22×C4C23×D17
FittingC23×C4⋊C4×C17C2
socleC24×C17C22⋊C4
prime radicalC25×C17C2×C4
cosocleC22×C4×C17C24
hypercenterC23×C4⋊C4D17
hypocenterC17C22×#324
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×C4⋊C4

1806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 135357);