Finite Group Databasebeta

C2×#14528538 #17031826

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC2×#14528538

Splittings

SylowC17 ⋊ C2×#1747

Subgroups

subgroupG/H
centerC2×C4C42×D17
commutatorC4×C17C22×C42
FrattiniC22×C4C23×D17
FittingC2×C17×H(3,ℤ/4)C2
socleC22×C17#376
prime radicalC24×C17#41
cosocleC22×C4×C17C24
hypercenterC2×H(3,ℤ/4)D17
hypocenterC17C2×#1747
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 167070);