Finite Group Databasebeta

C2×#14530080 #17062196

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

Aliases

direct productC2×#14530080

Splittings

SylowC17 ⋊ C2×#2052

Subgroups

subgroupG/H
centerC23#10587625
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC22×C17×#137C2
socleC23×C17#121
prime radicalC22×#41×C17C22
hypercenterC22×#137D17
hypocenterC17C2×#2052
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

1362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 197440);