Finite Group Databasebeta

C2×#14545170 #17978535

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14545170

Splittings

SylowC17 ⋊ C2×#2169

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC22×C17C23×C8
FrattiniC2×C4C23×#595
FittingC2×C17×C4⋊C8C4
socleC23×C17C22×C8
prime radicalC22×D68C8
cosocleC2×#3622C24
hypercenterC2×C4⋊C8#595
hypocenterC17C2×#2169
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 1113779);