Finite Group Databasebeta

C2×#14545594 #17979865

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14545594

Splittings

SylowC17 ⋊ C2×#2965

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C4×D4×C17C4
socleC23×C17C23×C4
prime radicalC22×#63254C4
cosocleC2×Dic17C25
hypercenterC2×C4×D4#595
hypocenterC17C2×#2965
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

2286 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, 1115109);