Finite Group Databasebeta

← Prev (#11719985) Next (#11719987) →

C2×C7×C61 #11719986

order854
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C32×C4×C5 (order 360) · Inn(G) = C1 · Out(G) = C2×C32×C4×C5
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC854
abelianC2×C7×C61

Subgroups

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

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 70
transitive degreeμt(G) = 854

A minimal faithful permutation representation — 1 generator 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

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

Relationships

center ofC7×Dic9×C61, C2×C7×D9×C61, C7×C3⋊Dic3×C61, …
Fitting subgroup ofDic7×C61, C7×Dic61, Dic427, …
socle ofDic7×C61, C7×Dic61, Dic427, …
maximal subgroup ofDic7×C61, C7×Dic61, Dic427, …
maximal normal subgroup ofDic7×C61, C7×Dic61, Dic427, …
maximal quotient ofC4×C7×C61, C22×C7×C61, C2×C3×C7×C61, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(854, 4);