Finite Group Databasebeta

C2×#14534366 #17205702

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14534366

Splittings

FittingC22×C4×D4×C17 ⋊ C2
SylowC17 ⋊ C2×#2600

Subgroups

subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC22×C4×D4×C17C2
socleC24×C17C24
prime radicalC2×#11762717C2
hypercenterC22×C4×D4D17
hypocenterC17C2×#2600
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4×D4

3502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 340946);