#559×C₇₁ #17985690

order	4544
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

#559×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₇₁
prime radical	#127×C₇₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ G

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 87 points:

(1,2,5,4)(3,7,8,6)(10,13)(14,15)(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);(2,4)(6,7)(9,10,12,13)(11,15,16,14);(1,3,5,8)(2,6,4,7);(1,4,5,2)(3,7,8,6)(9,11,12,16)(10,14,13,15)

Conjugacy classes & character table

1775 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×#1620, C₇₁×#1630, C₇₁×#1640, …
maximal normal subgroup of	C₇₁×#1620, C₇₁×#1630, C₇₁×#1640, …
maximal quotient of	C₇₁×#2355, C₇₁×#2357, C₇₁×#2366, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 240);

#559×C71 #17985690