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C31×C41 #11929651

order1271
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C3×C52×C8 (order 1200) · Inn(G) = C1 · Out(G) = C2×C3×C52×C8
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC1271
abelianC31×C41

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 72
transitive degreeμt(G) = 1271

A minimal faithful permutation representation — 1 generator on 72 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)

Conjugacy classes & character table

1271 conjugacy classes. The character table is too large to display.

Relationships

center ofA4×C31×C41, D7×C31×C41, D9×C31×C41, …
derived subgroup ofD1271, C3×Dic1271, C31⋊C3×Dic41, …
Fitting subgroup ofC41×D31, C31×D41, D1271, …
socle ofC41×D31, C31×D41, D1271, …
maximal subgroup ofC41×D31, C31×D41, D1271, …
maximal normal subgroup ofC41×D31, C31×D41, D1271, …
maximal quotient ofC2×C31×C41, C3×C31×C41, C11×C31×C41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1271, 1);