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C2×C3×C7×C292 #47977313

order35322
nilpotency class1
automorphism?
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29

Aliases

abelianC2×C3×C7×C292

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

256 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 70
transitive degreeμt(G) = 35322

A minimal faithful permutation representation — 2 generators on 70 points:

(1,2)(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)

Conjugacy classes & character table

35322 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35322, 17);