Finite Group Databasebeta

D17×#1384 #16949231

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productD17×#1384

Splittings

FittingC17×#1384 ⋊ C2
SylowC17 ⋊ C2×#1384

Subgroups

subgroupG/H
centerC4#106×D17
commutatorC8×C17C2×C42
FrattiniC22×C8C22×D17
FittingC17×#1384C2
socleC2×C17C2×#340
prime radicalC23×D17D8
cosocleC22×C8×C17C23
hypercenter#1384D17
hypocenterC17C2×#1384
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1384

586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84475);