Finite Group Databasebeta

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C23×C61 #13063868

order1403
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C3×C4×C5×C11 (order 1320) · Inn(G) = C1 · Out(G) = C2×C3×C4×C5×C11
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC1403
abelianC23×C61

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 84
transitive degreeμt(G) = 1403

A minimal faithful permutation representation — 1 generator on 84 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)

Conjugacy classes & character table

1403 conjugacy classes. The character table is too large to display.

Relationships

center ofD5×C23×C61, A4×C23×C61, D7×C23×C61, …
derived subgroup ofD1403, C5×D1403, D23×C61⋊C5, …
Fitting subgroup ofD23×C61, C23×D61, D1403, …
socle ofD23×C61, C23×D61, D1403, …
maximal subgroup ofD23×C61, C23×D61, D1403, …
maximal normal subgroup ofD23×C61, C23×D61, D1403, …
maximal quotient ofC2×C23×C61, C3×C23×C61, C11×C23×C61, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1403, 1);