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C3×#41×C29 #13063671

order1392
nilpotency class2
isoclinismisoclinic class of D4
automorphism?
homologyAbelianization (H1) = C23×C3×C29 · Schur multiplier (H2) = C22

Aliases

direct productC3×#41×C29

Subgroups

subgroupG/H
centerC3×C4×C29C22
commutator, Frattini, cosocleC2C23×C3×C29
socleC2×C3×C29C23
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C3×C4×C29 ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 696

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3)(4,5)(6,9)(7,8)(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);(5,8)(9,11);(4,6,7,10)(5,9,8,11)

Conjugacy classes & character table

870 conjugacy classes — view the full character table.

Relationships

maximal quotient ofC3×C4×D4×C29

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1392, 182);