Finite Group Databasebeta

← Prev (#89234) Next (#89236) →

Cayley diagram

C5×C89 #89235

order445
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C4×C8×C11 (order 352) · Inn(G) = C1 · Out(G) = C4×C8×C11
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC445
abelianC5×C89

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 94
transitive degreeμt(G) = 445

A minimal faithful permutation representation — 1 generator on 94 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)

Conjugacy classes & character table

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

Relationships

center ofC5×D3×C89, C5×D17×C89, C5×D32×C89, …
derived subgroup ofD445, Dic445, #13184067, …
Fitting subgroup ofD5×C89, C5×D89, D445, …
socle ofD5×C89, C5×D89, D445, …
maximal subgroup ofD5×C89, C5×D89, D445, …
maximal normal subgroup ofD5×C89, C5×D89, D445, …
maximal quotient ofC2×C5×C89, C3×C5×C89, C25×C89, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(445, 1);