Finite Group Databasebeta

C2×#14544728 #17969745

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14544728

Splittings

SylowC17 ⋊ C2×#1850

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC22×C17C23×C8
FrattiniC23C23×#595
FittingC22×C22⋊C4×C17C4
socleC24×C17C22×C4
prime radicalC25×C17C2×C4
cosocleC22×Dic17C24
hypercenterC22×C22⋊C4#595
hypocenterC17C2×#1850
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1104989);