Finite Group Databasebeta

C2×#14541917 #17940827

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

Aliases

direct productC2×#14541917

Splittings

FittingC2×C17×#508 ⋊ C2
SylowC17 ⋊ C2×#3414

Subgroups

subgroupG/H
centerC2×C4D8×D17
commutator, cosocleC8×C17C25
FrattiniC8C24×D17
FittingC2×C17×#508C2
socleC22×C17C22×D8
hypercenterC2×#508D17
hypocenterC17C2×#3414
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

2098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076071);