C₅×D₁₁×C₄₁ #17985227

order	4510
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×D₁₁×C₄₁

Splittings

Fitting, socle, Hall	C₅×C₁₁×C₄₁ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂×C₅×C₄₁
Hall	C₁₁×C₄₁ ⋊ C₂×C₅
Hall	C₅×C₁₁ ⋊ C₂×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₄₁	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₅×C₄₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₄₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₅×C₄₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2255

A minimal faithful permutation representation — 2 generators on 57 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);(7,16)(8,15)(9,14)(10,13)(11,12)

Conjugacy classes & character table

1435 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₅×D₁₁×C₄₁, C₅×C₄₁×D₃₃, D₁₁×C₂₅×C₄₁, …
maximal normal subgroup of	C₃×C₅×D₁₁×C₄₁, D₁₁×C₂₅×C₄₁, D₁₁×C₄₁⋊C₂₅, …
maximal quotient of	C₃×C₅×D₁₁×C₄₁, C₅×C₄₁×D₃₃, D₁₁×C₂₅×C₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4510, 9);

C5×D11×C41 #17985227