Finite Group Databasebeta

C4×#11762781 #17031973

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct productC4×#11762781

Splittings

FittingC4×C17×#99 ⋊ C2
SylowC17 ⋊ C4×#410

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D17
commutatorC22×C17C22×C42
FrattiniC24C23×D17
FittingC4×C17×#99C2
socleC22×C17C22×C22⋊C4
prime radicalC22×#63254C22
cosocleC24×C17C24
hypercenterC4×#99D17
hypocenterC17C4×#410
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

1666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 167217);