Finite Group Databasebeta

← Prev (#64434) Next (#64436) →

Cayley diagram

C5×C59 #64435

order295
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C4×C29 (order 232) · Inn(G) = C1 · Out(G) = C2×C4×C29
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC295
abelianC5×C59

Subgroups

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

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 64
transitive degreeμt(G) = 295

A minimal faithful permutation representation — 1 generator on 64 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)

Conjugacy classes & character table

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

Relationships

center ofC5×D3×C59, C5×D5×C59, C5×A4×C59, …
derived subgroup ofD295, Dic295, C59⋊AGL(1,𝔽5), …
Fitting subgroup ofD5×C59, C5×D59, D295, …
socle ofD5×C59, C5×D59, D295, …
maximal subgroup ofD5×C59, C5×D59, D295, …
maximal normal subgroup ofD5×C59, C5×D59, D295, …
maximal quotient ofC2×C5×C59, C3×C5×C59, C25×C59, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(295, 1);