Finite Group Databasebeta

C2×#14538316 #17901241

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14538316

Splittings

SylowC17 ⋊ C2×#3044

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×#137C2
socleC23×C17C22×D4
prime radicalC22×#41×C17C22
hypercenterC22×#137D17
hypocenterC17C2×#3044
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

2666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1036485);