Finite Group Databasebeta

C2×#14528732 #17033584

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

Aliases

direct productC2×#14528732

Splittings

SylowC17 ⋊ C2×#1790

Subgroups

subgroupG/H
centerC23#10587639
commutatorC23×C17C23×C4
FrattiniC24C23×D17
Fitting, prime radicalC22×C17×H(5,𝔽2)C2
socleC23×C17#120
cosocleC24×C17C24
hypercenterC22×H(5,𝔽2)D17
hypocenterC17C2×#1790
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C22×H(5,𝔽2)

4402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 168828);