Finite Group Databasebeta

C2×#14530215 #17063160

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

Aliases

direct productC2×#14530215

Splittings

SylowC17 ⋊ C2×#2076

Subgroups

subgroupG/H
centerC24C2×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#380C2
socleC24×C17C2×D4
prime radicalC25×C17D4
hypercenterC2×#380D17
hypocenterC17C2×#2076
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

1270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 198404);