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C7×C11×C43 #15693272

order3311
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C23×C32×C5×C7 (order 2520) · Inn(G) = C1 · Out(G) = C23×C32×C5×C7
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC3311
abelianC7×C11×C43

Subgroups

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

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 61
transitive degreeμt(G) = 3311

A minimal faithful permutation representation — 1 generator on 61 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)

Conjugacy classes & character table

3311 conjugacy classes. The character table is too large to display.

Relationships

center ofC7×D5×C11×C43
derived subgroup ofC5×D3311, C11⋊C5×D301, C7⋊(C43⋊AGL(1,𝔽11))
Fitting subgroup ofC7×C43×C11⋊C5, C11×C43⋊C49, C7×C11×C43⋊C7, …
socle ofC7×C43×C11⋊C5, C11×C43×C49, C11×C43⋊C49, …
maximal subgroup ofC5×C7×C11×C43, C7×C43×C11⋊C5, C11×C43×C49, …
maximal normal subgroup ofC5×C7×C11×C43, C7×C43×C11⋊C5, C11×C43×C49, …
maximal quotient ofC5×C7×C11×C43, C11×C43×C49, C72×C11×C43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3311, 2);