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C2×C7×C71 #11758586

order994
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C5×C7 (order 420) · Inn(G) = C1 · Out(G) = C22×C3×C5×C7
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC994
abelianC2×C7×C71

Subgroups

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

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 80
transitive degreeμt(G) = 994

A minimal faithful permutation representation — 1 generator on 80 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)

Conjugacy classes & character table

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

Relationships

center ofC7×Dic7×C71, C2×C7×D7×C71, C7×Dic9×C71, …
Fitting subgroup ofDic7×C71, C7×Dic71, Dic497, …
socle ofDic7×C71, C7×Dic71, Dic497, …
maximal subgroup ofDic7×C71, C7×Dic71, Dic497, …
maximal normal subgroup ofDic7×C71, C7×Dic71, Dic497, …
maximal quotient ofC4×C7×C71, C22×C7×C71, C2×C3×C7×C71, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(994, 6);