Finite Group Databasebeta

D17×#1296 #16924406

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productD17×#1296

Splittings

FittingC17×#1296 ⋊ C2
SylowC17 ⋊ C2×#1296

Subgroups

subgroupG/H
centerC23C22⋊C4×D17
commutatorC2×C4×C17C2×C42
FrattiniC2×C42C22×D17
FittingC17×#1296C2
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC2×C42×C17C23
hypercenter#1296D17
hypocenterC17C2×#1296
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 59650);