#474×C₇₁ #17985605

order	4544
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#474×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

108 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)(12,15)(14,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(1,3,4,8)(2,5,6,7);(10,13)(11,16)(14,15)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇₁×#1639, C₇₁×#1641, C₇₁×#1644, …
maximal normal subgroup of	C₇₁×#1639, C₇₁×#1641, C₇₁×#1644, …
maximal quotient of	C₇₁×#1802, C₇₁×#1862, C₇₁×#1918, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 155);

#474×C71 #17985605