Finite Group Databasebeta

C2×#14541930 #17940842

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

Aliases

direct productC2×#14541930

Splittings

FittingC2×C17×#509 ⋊ C2
SylowC17 ⋊ C2×#3416

Subgroups

subgroupG/H
centerC22C2×D8×D17
commutator, cosocleC8×C17C25
FrattiniC8C24×D17
FittingC2×C17×#509C2
socleC22×C17C22×D8
hypercenterC2×#509D17
hypocenterC17C2×#3416
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

2074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076086);