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C23×C67 #13095382

order1541
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C112 (order 1452) · Inn(G) = C1 · Out(G) = C22×C3×C112
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC1541
abelianC23×C67

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 90
transitive degreeμt(G) = 1541

A minimal faithful permutation representation — 1 generator on 90 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90)

Conjugacy classes & character table

1541 conjugacy classes. The character table is too large to display.

Relationships

center ofD5×C23×C67, A4×C23×C67, D7×C23×C67, …
derived subgroup ofD1541, C5×D1541, #30683987, …
Fitting subgroup ofD23×C67, C23×D67, D1541, …
socle ofD23×C67, C23×D67, D1541, …
maximal subgroup ofD23×C67, C23×D67, D1541, …
maximal normal subgroup ofD23×C67, C23×D67, D1541, …
maximal quotient ofC2×C23×C67, C3×C23×C67, C11×C23×C67, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1541, 1);