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Cayley diagram

C4×C61 #6922

order244
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C3×C4×C5 (order 120) · Inn(G) = C1 · Out(G) = C2×C3×C4×C5
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC244
abelianC4×C61

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C61
socle, prime radicalC2×C61C2
LCSG ▷ C1
UCSC1 ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 65
transitive degreeμt(G) = 244

A minimal faithful permutation representation — 1 generator on 65 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)

Conjugacy classes & character table

244 conjugacy classes — view the full character table.

Relationships

center ofM16×C61, #41×C61, C3⋊C8×C61, …
derived subgroup of#11758190, D488, Dic244, …
Frattini subgroup ofDic14884, D29768
Fitting subgroup of#92418, Dic122, C4×D61, …
maximal subgroup of#92418, C8×C61, Dic122, …
maximal normal subgroup of#92418, C8×C61, Dic122, …
maximal quotient ofC8×C61, C2×C4×C61, Dic3×C61, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(244, 2);