#350×C₇₁ #17985481

order	4544
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₇₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

#350×C₇₁

Subgroups

	subgroup	G/H
center	C₈×C₇₁	D₄
commutator	C₄	C₂×C₈×C₇₁
Frattini, cosocle	C₂×C₈	C₂²×C₇₁
socle	C₂×C₇₁	C₂²⋊C₈
prime radical	#41×C₇₁	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×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:

(1,2,5,10,6,11,20,28,7,12,21,29,4,9,18,26)(3,13,15,30,14,24,31,27,16,25,19,32,17,8,22,23)(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)(5,19)(6,14)(7,16)(9,25)(10,27)(11,13)(12,24)(15,21)(18,31)(20,22)(23,29)(26,30)(28,32)

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×#350×C₇₁, C₇₁×#2117, C₇₁×#2170, …
maximal normal subgroup of	C₂×#350×C₇₁, C₇₁×#2117, C₇₁×#2170, …
maximal quotient of	C₇₁×#1315, C₇₁×#1323, C₇₁×D₄⋊C₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 31);

#350×C71 #17985481