Finite Group Databasebeta

D17×#2158 #17187349

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD17×#2158

Splittings

FittingC17×#2158 ⋊ C2
SylowC17 ⋊ C2×#2158

Subgroups

subgroupG/H
centerC2×C4D8×D17
commutatorC8×C17C23×C4
FrattiniC2×C8C23×D17
FittingC17×#2158C2
socleC22×C17C22×D8
prime radicalC23×D17D8
cosocleC2×C8×C17C24
hypercenter#2158D17
hypocenterC17C2×#2158
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2158

694 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, 322593);