Finite Group Databasebeta

← Prev (#11725228) Next (#11725230) →

C19×C47 #11725229

order893
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C9×C23 (order 828) · Inn(G) = C1 · Out(G) = C22×C9×C23
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC893
abelianC19×C47

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 66
transitive degreeμt(G) = 893

A minimal faithful permutation representation — 1 generator on 66 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)

Conjugacy classes & character table

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

Relationships

center ofD9×C19×C47, C3⋊D3×C19×C47, C19×AGL(1,𝔽5)×C47, …
derived subgroup ofD893, Dic893, D19×D47, …
Fitting subgroup ofD19×C47, C19×D47, D893, …
socle ofD19×C47, C19×D47, D893, …
maximal subgroup ofD19×C47, C19×D47, D893, …
maximal normal subgroup ofD19×C47, C19×D47, D893, …
maximal quotient ofC2×C19×C47, C3×C19×C47, C5×C19×C47, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(893, 1);