Finite Group Databasebeta

C2×#14540548 #17910503

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14540548

Splittings

FittingC2×C17×#576 ⋊ C2
SylowC17 ⋊ C2×#3288

Subgroups

subgroupG/H
centerC22D4×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#576C2
socleC22×C17D42
hypercenterC2×#576D17
hypocenterC17C2×#3288
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#576

2704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 1045747);