C₂×C₅×D₁₁×C₆₁ #27211908

order	13420
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₆₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂×C₅×D₁₁×C₆₁

Splittings

Fitting, socle	C₂×C₅×C₁₁×C₆₁ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂²×C₅×C₆₁
Hall	C₅×C₁₁×C₆₁ ⋊ C₂²
Hall	C₁₁×C₆₁ ⋊ C₂²×C₅
Hall	C₅×C₁₁ ⋊ C₂²×C₆₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₆₁	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₅×C₆₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₆₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅×C₆₁

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 6710

A minimal faithful permutation representation — 2 generators on 79 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72)(73,74,75,76,77);(1,2,4,6,8,10,11,9,7,5,3)(78,79)

Conjugacy classes & character table

4270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13420, 100);

C2×C5×D11×C61 #27211908