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Cayley diagram

D3×C71 #88338

order426
isoclinismisoclinic class of D3
automorphismAut(G) = C2×C5×D3×C7 (order 420) · Inn(G) = D3 · Out(G) = C2×C5×C7
homologyAbelianization (H1) = C2×C71 · Schur multiplier (H2) = C1

Aliases

direct productD3×C71
unambiguous semidirect productC3⋊(C2×C71)

Splittings

Fitting, socle, HallC3×C71 ⋊ C2
derived, SylowC3 ⋊ C2×C71

Subgroups

subgroupG/H
center, hypercenterC71D3
commutator, cosocle, hypocenterC3C2×C71
FrattiniC1G
Fitting, socleC3×C71C2
LCSG ▷ C3
UCSC1 ◁ C71

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 74
transitive degreeμt(G) = 213

A minimal faithful permutation representation — 2 generators on 74 points:

(2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74);(1,2,3)

Conjugacy classes & character table

213 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D71, C2×D3×C71, D9×C71, …
maximal normal subgroup ofD3×D71, C2×D3×C71, C3×D3×C71, …
maximal quotient ofDic3×C71, C2×D3×C71, D9×C71, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(426, 1);