Finite Group Databasebeta

C2×#14538000 #17900659

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#14538000

Splittings

FittingC2×C17×#525 ⋊ C2
SylowC17 ⋊ C2×#3002

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#525C2
socleC23×C17C22×D4
hypercenterC2×#525D17
hypocenterC17C2×#3002
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×#525

5130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

524 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1035903);