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Cayley diagram

C5×C79 #87668

order395
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C3×C4×C13 (order 312) · Inn(G) = C1 · Out(G) = C2×C3×C4×C13
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC395
abelianC5×C79

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 84
transitive degreeμt(G) = 395

A minimal faithful permutation representation — 1 generator on 84 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84)

Conjugacy classes & character table

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

Relationships

center ofC5×D3×C79, C5×D5×C79, C5×D32×C79, …
derived subgroup ofD395, Dic395, C79⋊AGL(1,𝔽5), …
Fitting subgroup ofD5×C79, C5×D79, D395, …
socle ofD5×C79, C5×D79, D395, …
maximal subgroup ofD5×C79, C5×D79, D395, …
maximal normal subgroup ofD5×C79, C5×D79, D395, …
maximal quotient ofC2×C5×C79, C3×C5×C79, C25×C79, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(395, 1);