#478×C₇₁ #17985609

order	4544
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

#478×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₇₁
prime radical	C₂×D₄×C₇₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₄²×C₇₁ ◁ G

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 2272

A minimal faithful permutation representation — 3 generators on 87 points:

(1,2,4,6)(3,7,8,5)(9,10,11,13)(12,14,16,15)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(1,3,4,8)(2,5,6,7)(10,13)(14,15);(10,14)(12,16)(13,15)

Conjugacy classes & character table

1349 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×#478×C₇₁, C₇₁×#3076, C₇₁×#3077, …
maximal normal subgroup of	C₂×#478×C₇₁, C₇₁×#3076, C₇₁×#3077, …
maximal quotient of	C₇₁×#1804, C₇₁×#1862, C₇₁×#1864, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 159);

#478×C71 #17985609