Finite Group Databasebeta

C2×#14530764 #17188273

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

Aliases

direct productC2×#14530764

Splittings

FittingC2×C17×#350 ⋊ C2
SylowC17 ⋊ C2×#2195

Subgroups

subgroupG/H
centerC22#11762945
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC2×C17×#350C2
socleC22×C17#447
prime radicalC2×#11763626C2
hypercenterC2×#350D17
hypocenterC17C2×#2195
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#350

1078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 323517);