Finite Group Databasebeta

C2×#131×#595 #17979418

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#131×#595

Splittings

FittingC2×C17×#131 ⋊ C4
SylowC17 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC2×C8C22×#595
commutatorC2×C17C23×C42
FrattiniC4C24×#595
FittingC2×C17×#131C4
socleC22×C17C22×C42
prime radicalC2×#41×D17C22
cosocleC4×D17C25
hypercenterC2×#131#595
hypocenterC17C2×C4×#131
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C2×#131

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114662);