Finite Group Databasebeta

C2×#14544316 #17966129

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

Aliases

direct productC2×#14544316

Splittings

SylowC17 ⋊ C2×#1557

Subgroups

subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×#121C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#11763354C2
cosocleC4×Dic17C24
hypercenterC2×#121#595
hypocenterC17C2×#1557
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

1278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1101373);