Finite Group Databasebeta

C2×#14545126 #17978417

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

Aliases

direct productC2×#14545126

Splittings

SylowC17 ⋊ C2×#2153

Subgroups

subgroupG/H
centerC2×C4C2×C4⋊#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
FittingC2×C17×#97C4
socleC22×C17C2×C4⋊C8
prime radicalC23×D17M16
cosocleC2×#3622C24
hypercenterC2×#97#595
hypocenterC17C2×#2153
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#97

698 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, 1113661);