Finite Group Databasebeta

C2×#14545174 #17978575

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

Aliases

direct productC2×#14545174

Splittings

SylowC17 ⋊ C2×#2171

Subgroups

subgroupG/H
centerC2×C4D4×#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
Fitting, prime radicalC2×C17×#135C4
socleC22×C17C8×D4
cosocleC2×#3622C24
hypercenterC2×#135#595
hypocenterC17C2×#2171
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113819);