Finite Group Databasebeta

C2×#14545020 #17978189

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14545020

Splittings

SylowC17 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC22×C17C23×C8
FrattiniC2×C4C23×#595
Fitting, prime radicalC22×#41×C17C4
socleC22×C17C2×C22⋊C8
cosocleC2×#3622C24
hypercenterC22×#41#595
hypocenterC17C2×#2115
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113433);