Finite Group Databasebeta

C2×#14528698 #17033446

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14528698

Splittings

FittingC2×C17×#379 ⋊ C2
SylowC17 ⋊ C2×#1781

Subgroups

subgroupG/H
centerC23C2×#63227
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C17×#379C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C22⋊D17C2
cosocleC24×C17C24
hypercenterC2×#379D17
hypocenterC17C2×#1781
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C26 ◁ C2×#379

6254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 168690);