Finite Group Databasebeta

C2×#14528889 #17034169

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14528889

Splittings

SylowC17 ⋊ C2×#1827

Subgroups

subgroupG/H
centerC2×C4#10587563
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#413C2
socleC22×C17#381
prime radicalC22×#41×C17C22
cosocleC22×C4×C17C24
hypercenterC2×#413D17
hypocenterC17C2×#1827
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

1354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 169413);