Finite Group Databasebeta

D17×#1305 #16924652

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

Aliases

direct productD17×#1305

Splittings

FittingC17×#1305 ⋊ C2
SylowC17 ⋊ C2×#1305

Subgroups

subgroupG/H
centerC22#95×D17
commutatorC23×C17C2×C42
FrattiniC23×C4C22×D17
FittingC17×#1305C2
socleC22×C17C2×#95
prime radicalC24×D17C2×C4
cosocleC23×C4×C17C23
hypercenter#1305D17
hypocenterC17C2×#1305
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

986 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, 59896);