C₇×C₁₁×C₄₉ #16836833

order	3773
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 123480
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

abelian

C₇×C₁₁×C₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₇²×C₁₁
socle, prime radical	C₇²×C₁₁	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 3773

A minimal faithful permutation representation — 2 generators on 67 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)(57,58,59,60,61,62,63,64,65,66,67);(50,51,52,53,54,55,56)

Conjugacy classes & character table

3773 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁×C₄₉², C₁₁×C₇²⋊C₄₉, C₁₁×C₄₉⋊C₄₉, …
maximal normal subgroup of	C₁₁×C₄₉², C₁₁×C₇²⋊C₄₉, C₁₁×C₄₉⋊C₄₉, …
maximal quotient of	C₁₁×C₄₉², C₁₁×C₇²⋊C₄₉, C₁₁×C₄₉⋊C₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3773, 2);

C7×C11×C49 #16836833