Finite Group Databasebeta

C4×#11763676 #17956595

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C43

Aliases

direct productC4×#11763676

Splittings

FittingC43×C17 ⋊ C4
SylowC17 ⋊ C4×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC42C4×#595
commutatorC4×C17C43
FrattiniC22×C4C22×#595
FittingC43×C17C4
socleC22×C17C2×#95
prime radicalC23×D17C2×D4
cosocleC22×C4×D17C23
hypercenterC43#595
hypocenterC17C4×H(3,ℤ/4)
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C42 ◁ C43

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1091839);