Finite Group Databasebeta

C4×#11763761 #17962949

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C42

Aliases

direct productC4×#11763761

Splittings

FittingC2×C4×D4×C17 ⋊ C4
SylowC17 ⋊ C4×#390

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC22×C17C22×C42
FrattiniC23C23×#595
FittingC2×C4×D4×C17C4
socleC23×C17C23×C4
prime radicalC22×D4×D17C22
cosocleC23×D17C24
hypercenterC2×C4×D4#595
hypocenterC17C4×#390
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1098193);