Finite Group Databasebeta

C2×#14528272 #17016830

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14528272

Splittings

FittingC2×C17×#332 ⋊ C2
SylowC17 ⋊ C2×#1689

Subgroups

subgroupG/H
centerC23#10587570
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC2×C17×#332C2
socleC23×C17#121
prime radicalC22×D68D4
hypercenterC2×#332D17
hypocenterC17C2×#1689
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 152074);