#347×C₇₁ #17985478

order	4544
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₇₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

#347×C₇₁

Subgroups

	subgroup	G/H
center	C₄×C₇₁	C₄²
commutator	C₄	C₄²×C₇₁
Frattini, cosocle	C₂×C₈	C₂²×C₇₁
socle	C₂×C₇₁	#97
prime radical	C₂²×C₇₁	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₇₁ ◁ G

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 87 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇₁×#1355, C₇₁×#1356, C₂×#347×C₇₁, …
maximal normal subgroup of	C₇₁×#1355, C₇₁×#1356, C₂×#347×C₇₁, …
maximal quotient of	C₇₁×#1313, C₇₁×#1375, C₂×#347×C₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 28);

#347×C71 #17985478