Finite Group Databasebeta

D17×#1381 #16949209

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

Aliases

direct productD17×#1381

Splittings

FittingC17×#1381 ⋊ C2
SylowC17 ⋊ C2×#1381

Subgroups

subgroupG/H
centerC2×C4D8×D17
commutatorC8×C17C2×C42
FrattiniC22×C8C22×D17
FittingC17×#1381C2
socleC22×C17C2×#107
prime radicalC23×D17Q16
cosocleC22×C8×C17C23
hypercenter#1381D17
hypocenterC17C2×#1381
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1381

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84453);