Finite Group Databasebeta

C4×#11762906 #17032812

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11762906

Splittings

SylowC17 ⋊ C4×#440

Subgroups

subgroupG/H
centerC22×C4D4×D17
commutatorC4×C17C22×C42
FrattiniC22×C4C23×D17
FittingC4×C17×#102C2
socleC23×C17C22×D4
prime radicalC22×D4×C17C23
cosocleC22×C4×C17C24
hypercenterC4×#102D17
hypocenterC17C4×#440
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

1206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 168056);