Finite Group Databasebeta

C2×#14544272 #17965849

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14544272

Splittings

SylowC17 ⋊ C2×#1536

Subgroups

subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC22×#41×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#11763355C2
cosocleC4×Dic17C24
hypercenterC22×#41#595
hypocenterC17C2×#1536
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

1234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1101093);