#359×C₇₁ #17985490

order	4544
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

#359×C₇₁

Subgroups

	subgroup	G/H
center	C₄×C₇₁	D₈
commutator	C₈	C₂×C₄×C₇₁
Frattini, cosocle	C₂×C₈	C₂²×C₇₁
socle	C₂×C₇₁	#102
prime radical	#135×C₇₁	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₁ ◁ C₂×C₄×C₇₁ ◁ C₂×C₈×C₇₁ ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 103
transitive degree	μ_t(G) = 2272

A minimal faithful permutation representation — 2 generators on 103 points:

(1,2,5,10,7,11,6,21)(3,12,14,28,15,29,22,26)(4,16,18,27,20,31,19,9)(8,17,23,30,25,32,24,13)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,3)(2,8)(4,17)(5,14)(6,22)(7,15)(9,26)(10,23)(11,25)(12,16)(13,19)(18,30)(20,32)(21,24)(27,28)(29,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×#359×C₇₁, C₇₁×#2143, C₇₁×#2178, …
maximal normal subgroup of	C₂×#359×C₇₁, C₇₁×#2143, C₇₁×#2178, …
maximal quotient of	C₇₁×#1331, C₇₁×#1332, C₇₁×#1349, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 40);

#359×C71 #17985490