Finite Group Databasebeta

C2×#14529784 #17061111

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14529784

Splittings

FittingC23×SD16×C17 ⋊ C2
SylowC17 ⋊ C2×#2000

Subgroups

subgroupG/H
centerC24D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC23×SD16×C17C2
socleC24×C17C2×D4
prime radicalC22×#10587624C2
hypercenterC23×SD16D17
hypocenterC17C2×#2000
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×SD16

2526 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, 196355);