Finite Group Databasebeta

C2×#14532020 #17200542

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

Aliases

direct productC2×#14532020

Splittings

FittingC22×C17×#117 ⋊ C2
SylowC17 ⋊ C2×#2392

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC22×C17×#117C2
socleC24×C17C24
prime radicalC2×#11762718C2
hypercenterC22×#117D17
hypocenterC17C2×#2392
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×#117

4134 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, 335786);