Finite Group Databasebeta

C2×#14544026 #17964216

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14544026

Splittings

SylowC17 ⋊ C2×#1461

Subgroups

subgroupG/H
centerC22×C4C22⋊#595
commutatorC22×C17C23×C8
FrattiniC23C23×#595
FittingC22×C42×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22×C4
cosocleC22×Dic17C24
hypercenterC22×C42#595
hypocenterC17C2×#1461
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

1282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1099460);