Finite Group Databasebeta

C2×#14539423 #17904146

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

Aliases

direct productC2×#14539423

Splittings

FittingC2×C17×#405 ⋊ C2
SylowC17 ⋊ C2×#3175

Subgroups

subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#405C2
socleC23×C17C22×D4
prime radicalC2×#11763045C2
hypercenterC2×#405D17
hypocenterC17C2×#3175
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

1970 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, 1039390);