C₅×C₁₁×#6923 #27211884

order	13420
isoclinism	isoclinic class of #6923
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×C₁₁×#6923

Splittings

Fitting, socle, Hall	C₅×C₁₁×C₆₁ ⋊ C₄
derived, Sylow	C₆₁ ⋊ C₄×C₅×C₁₁
Hall	C₁₁×C₆₁ ⋊ C₄×C₅
Hall	C₅×C₆₁ ⋊ C₄×C₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₁₁	#6923
commutator, hypocenter	C₆₁	C₄×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₆₁	C₄
prime radical	C₅×C₁₁×D₆₁	C₂
cosocle	D₆₁	C₂×C₅×C₁₁
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₅×C₁₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 3355

A minimal faithful permutation representation — 2 generators on 77 points:

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

Conjugacy classes & character table

1045 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13420, 76);

C5×C11×#6923 #27211884