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C16×C59 #11745657

order944
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C4×C29 (order 464) · Inn(G) = C1 · Out(G) = C22×C4×C29
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC944
abelianC16×C59

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C2×C59
socle, prime radicalC2×C59C8
LCSG ▷ C1
UCSC1 ◁ G

10 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 75
transitive degreeμt(G) = 944

A minimal faithful permutation representation — 1 generator on 75 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)

Conjugacy classes & character table

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

Relationships

center ofC59×M64, C59×#504, C59×#7381, …
derived subgroup of#16837237, D1888, #16837239, …
Fitting subgroup ofC59⋊C32, C16×D59, #14273666, …
maximal subgroup ofC32×C59, C2×C16×C59, M32×C59, …
maximal normal subgroup ofC32×C59, C2×C16×C59, M32×C59, …
maximal quotient ofC32×C59, C2×C16×C59, C3×C16×C59, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(944, 2);