Finite Group Databasebeta

← Prev (#17193603) Next (#17193605) →

D4×C4⋊C4×D17 #17193604

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD4×C4⋊C4×D17

Splittings

FittingD4×C4⋊C4×C17 ⋊ C2
SylowC17 ⋊ C2×D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingD4×C4⋊C4×C17C2
socle, cosocleC23×C17C25
prime radicalC22×D4×D17C22
hypercenterD4×C4⋊C4D17
hypocenterC17C2×D4×C4⋊C4
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ D4×C4⋊C4

4718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 328848);