Finite Group Databasebeta

D17×#1395 #16949313

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD17×#1395

Splittings

FittingC17×#1395 ⋊ C2
SylowC17 ⋊ C2×#1395

Subgroups

subgroupG/H
centerC4#99×D17
commutatorC2×C4×C17C2×C42
FrattiniC2×#41C22×D17
FittingC17×#1395C2
socleC2×C17C2×#342
prime radicalC2×#41×D17C22
cosocleC2×#41×C17C23
hypercenter#1395D17
hypocenterC17C2×#1395
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1395

766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84557);