#576×C₇₁ #17985707

order	4544
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

#576×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₁	C₂²×D₄
commutator, Frattini, cosocle	C₄	C₂⁴×C₇₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₁ ◁ #41×C₇₁ ◁ G

268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 1136

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

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

Conjugacy classes & character table

1562 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×#2192, C₇₁×#2194, C₇₁×#3288, …
maximal normal subgroup of	C₇₁×#2192, C₇₁×#2194, C₇₁×#3288, …
maximal quotient of	C₇₁×#2897, C₇₁×#2913, C₇₁×#2946, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 257);

#576×C71 #17985707