Finite Group Databasebeta

C2×#14529931 #17061601

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14529931

Splittings

FittingC2×C17×#336 ⋊ C2
SylowC17 ⋊ C2×#2025

Subgroups

subgroupG/H
centerC24C2×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#336C2
socleC24×C17C2×D4
prime radicalC23×D68C22
hypercenterC2×#336D17
hypocenterC17C2×#2025
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

1518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 196845);