Finite Group Databasebeta

C2×#14530778 #17188337

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14530778

Splittings

FittingC2×C17×#458 ⋊ C2
SylowC17 ⋊ C2×#2198

Subgroups

subgroupG/H
centerC22#11762995
commutator, cosocleC2×D4×C17C24
FrattiniC2×D4C23×D17
FittingC2×C17×#458C2
socleC22×C17B(4,𝔽2)
prime radicalC2×#11762977C2
hypercenterC2×#458D17
hypocenterC17C2×#2198
LCSG ▷ C2×D4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#458

1244 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 323581);