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C19×C101 #14274302

order1919
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C4×C9×C25 (order 1800) · Inn(G) = C1 · Out(G) = C2×C4×C9×C25
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC1919
abelianC19×C101

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 120
transitive degreeμt(G) = 1919

A minimal faithful permutation representation — 1 generator on 120 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)

Conjugacy classes & character table

1919 conjugacy classes. The character table is too large to display.

Relationships

center ofD5×C19×C101, A4×C19×C101, D7×C19×C101, …
derived subgroup ofD1919, C5×D1919, D19×C101⋊C5, …
Fitting subgroup ofD19×C101, C19×D101, D1919, …
socle ofD19×C101, C19×D101, D1919, …
maximal subgroup ofD19×C101, C19×D101, D1919, …
maximal normal subgroup ofD19×C101, C19×D101, D1919, …
maximal quotient ofC2×C19×C101, C7×C19×C101, C11×C19×C101, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1919, 1);