Finite Group Databasebeta

C2×#14544558 #17968462

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14544558

Splittings

FittingC2×C17×#131 ⋊ C4
SylowC17 ⋊ C2×#1764

Subgroups

subgroupG/H
centerC2×C8C22⋊#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC2×C17×#131C4
socleC22×C17C4×C22⋊C4
prime radicalC2×#41×D17C22
cosocleC2×C4×D17C24
hypercenterC2×#131#595
hypocenterC17C2×#1764
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

1558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103706);