Finite Group Databasebeta

D17×#479 #14538557

order2176
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productD17×#479

Splittings

FittingC17×#479 ⋊ C2
SylowC17 ⋊ C2×#479

Subgroups

subgroupG/H
centerC22C2×D4×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#479C2
socleC22×C17C22×D4
prime radicalC22×D17C2×D4
hypercenter#479D17
hypocenterC17C2×#479
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #479

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D17×#479, D17×#3076, D17×#3078, …
maximal normal subgroup ofC2×D17×#479, D17×#3076, D17×#3078, …
maximal quotient ofD17×#1805, D17×#1863, D17×#1865, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 14283);