C₁₁×#11925882 #27210841

order	13299
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₁×#11925882

Splittings

Fitting, socle, Hall	C₁₁×C₁₃×C₃₁ ⋊ C₃
derived, Hall	C₁₃×C₃₁ ⋊ C₃×C₁₁
Hall	C₁₁×C₃₁ ⋊ C₁₃⋊C₃
Hall	C₁₁×C₁₃ ⋊ C₃₁⋊C₃
Sylow	C₃₁ ⋊ C₁₁×C₁₃⋊C₃
Sylow	C₁₃ ⋊ C₁₁×C₃₁⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	#11925882
commutator, cosocle, hypocenter	C₁₃×C₃₁	C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₃₁	C₃
LCS	G ▷ C₁₃×C₃₁
UCS	C₁ ◁ C₁₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 4433

A minimal faithful permutation representation — 2 generators on 55 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,21)(11,15,18)(13,19,16)(17,24,27)(20,26,25)(22,28,23)(29,31,30)(33,34,36)(35,38,42)(37,40,39)(41,43,44)(45,46,47,48,49,50,51,52,53,54,55);(1,2,4,8,15,3,6,11,17,24,7,13,20,21,27,14,22,29,28,12,18,25,30,31,19,5,9,16,23,26,10)(32,33,35,36,39,38,42,44,43,34,37,41,40)

Conjugacy classes & character table

1507 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₁×#11925882, C₁₁×#14559022, C₁₁×#14559026, …
maximal normal subgroup of	C₂×C₁₁×#11925882, C₁₁×#14559022, C₁₁×#14559026, …
maximal quotient of	C₂×C₁₁×#11925882

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13299, 4);

C11×#11925882 #27210841