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Cayley diagram

C3×C22⋊D17 #87982

order408
isoclinismisoclinic class of Dic34
automorphismAut(G) = C23×AGL(1,𝔽17) (order 2176) · Inn(G) = C2×D17 · Out(G) = C2×C16
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×C22⋊D17

Splittings

FittingC22×C3×C17 ⋊ C2
HallC3×C17 ⋊ D4
SylowC17 ⋊ C3×D4

Subgroups

subgroupG/H
centerC2×C3C2×D17
commutator, cosocleC2×C17C22×C3
FrattiniC2C2×C3×D17
FittingC22×C3×C17C2
socleC2×C3×C17C22
hypercenterC22×C3D17
hypocenterC17C3×D4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C3 ◁ C22×C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 204

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(19,21)(22,23,24);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)

Conjugacy classes & character table

111 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11717866, #11717867, D3×C22⋊D17, …
maximal normal subgroup of#11717866, #11717867, D3×C22⋊D17, …
maximal quotient ofC3×#63225, C3×#63227, C3×#63228, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 19);