#473×C₇₁ #17985604

order	4544
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#473×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₁	#121
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₇₁
prime radical	#41×C₇₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₁ ◁ C₂×C₄×C₇₁ ◁ G

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 103 points:

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

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×#2194, C₇₁×#2195, C₇₁×#2222, …
maximal normal subgroup of	C₇₁×#2194, C₇₁×#2195, C₇₁×#2222, …
maximal quotient of	C₇₁×#1669, C₇₁×#1670, C₇₁×#1673, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 154);

#473×C71 #17985604