#366×C₇₁ #17985497

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

Aliases

direct product

#366×C₇₁

Subgroups

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

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 4544

A minimal faithful permutation representation — 2 generators on 91 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇₁×#1415, C₇₁×#1416, C₇₁×#1423, …
maximal normal subgroup of	C₇₁×#1415, C₇₁×#1416, C₇₁×#1423, …
maximal quotient of	C₇₁×#1371, C₇₁×#1380, C₇₁×#1423, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 47);

#366×C71 #17985497