C₁₃×D₁₁×C₄₃ #27134133

order	12298
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₁₁×C₄₃
unambiguous semidirect product	C₁₁⋊(C₂×C₁₃×C₄₃)

Splittings

Fitting, socle, Hall	C₁₁×C₁₃×C₄₃ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂×C₁₃×C₄₃
Hall	C₁₁×C₄₃ ⋊ C₂×C₁₃
Hall	C₁₁×C₁₃ ⋊ C₂×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃×C₄₃	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₁₃×C₄₃
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₄₃	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₁₃×C₄₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 6149

A minimal faithful permutation representation — 2 generators on 67 points:

(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);(1,2,4,6,8,10,11,9,7,5,3)

Conjugacy classes & character table

3913 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₃×D₁₁×D₄₃, D₁₁×D₁₃×C₄₃, D₁₁×D₅₅₉, …
maximal normal subgroup of	C₁₃×D₁₁×D₄₃, D₁₁×D₁₃×C₄₃, D₁₁×D₅₅₉, …
maximal quotient of	C₁₃×C₄₃×Dic₁₁, C₂×C₁₃×D₁₁×C₄₃, C₃×C₁₃×D₁₁×C₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12298, 5);

C13×D11×C43 #27134133