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C31×C47 #13089926

order1457
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C5×C23 (order 1380) · Inn(G) = C1 · Out(G) = C22×C3×C5×C23
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC1457
abelianC31×C47

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 78
transitive degreeμt(G) = 1457

A minimal faithful permutation representation — 1 generator on 78 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)

Conjugacy classes & character table

1457 conjugacy classes. The character table is too large to display.

Relationships

center ofD5×C31×C47, A4×C31×C47, D7×C31×C47, …
derived subgroup ofD1457, C5×D1457, D47×ΓL(1,𝔽32), …
Fitting subgroup ofC47×D31, C31×D47, D1457, …
socle ofC47×D31, C31×D47, D1457, …
maximal subgroup ofC47×D31, C31×D47, D1457, …
maximal normal subgroup ofC47×D31, C31×D47, D1457, …
maximal quotient ofC2×C31×C47, C3×C31×C47, C11×C31×C47, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1457, 1);