Finite Group Databasebeta

C2×#14537998 #17900657

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

Aliases

direct productC2×#14537998

Splittings

FittingC22×C17×#135 ⋊ C2
SylowC17 ⋊ C2×#3002

Subgroups

subgroupG/H
centerC22×C4D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×#135C2
socleC23×C17C22×D4
hypercenterC22×#135D17
hypocenterC17C2×#3002
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#135

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, 1035901);