Finite Group Databasebeta

D17×#1876 #17035604

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD17×#1876

Splittings

FittingC17×#1876 ⋊ C2
SylowC17 ⋊ C2×#1876

Subgroups

subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1876C2
socleC22×C17C2×C4×D4
prime radicalC2×#135×D17C2
cosocleC22×C4×C17C24
hypercenter#1876D17
hypocenterC17C2×#1876
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

1754 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 170848);