Finite Group Databasebeta

C2×#14533847 #17204406

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14533847

Splittings

FittingC2×C17×#398 ⋊ C2
SylowC17 ⋊ C2×#2554

Subgroups

subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#398C2
socleC24×C17C24
prime radicalC2×#11762719C2
hypercenterC2×#398D17
hypocenterC17C2×#2554
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#398

3158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 339650);