Finite Group Databasebeta

C2×#14536909 #17240644

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#14536909

Splittings

FittingC2×C17×#394 ⋊ C2
SylowC17 ⋊ C2×#2829

Subgroups

subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#394C2
socleC24×C17C24
prime radicalC2×#11762717C2
hypercenterC2×#394D17
hypocenterC17C2×#2829
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#394

2434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 375888);