#442×C₇₁ #17985573

order	4544
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

#442×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂×D₄
commutator	C₄	C₂²×C₄×C₇₁
Frattini, cosocle	C₂×C₄	C₂³×C₇₁
prime radical	C₂×D₈×C₇₁	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₄²×C₇₁ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 2272

A minimal faithful permutation representation — 3 generators on 83 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇₁×AGL(1,ℤ/16), C₂×#442×C₇₁, C₇₁×#2943, …
maximal normal subgroup of	C₇₁×AGL(1,ℤ/16), C₂×#442×C₇₁, C₇₁×#2943, …
maximal quotient of	C₇₁×#1580, C₇₁×#1586, C₇₁×#1594, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 123);

#442×C71 #17985573