Finite Group Databasebeta

D17×#1279 #16923846

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productD17×#1279

Splittings

FittingC17×#1279 ⋊ C2
SylowC17 ⋊ C2×#1279

Subgroups

subgroupG/H
centerC22×C4D4×D17
commutatorC4×C17C2×C4×C8
FrattiniC2×C42C22×D17
FittingC17×#1279C2
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C42×C17C23
hypercenter#1279D17
hypocenterC17C2×#1279
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 59090);