C₂×#126×C₇₁ #17985659

order	4544
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×#126×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₇₁
prime radical	C₂⁴×C₇₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ G

246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 89
transitive degree	μ_t(G) = 2272

A minimal faithful permutation representation — 4 generators on 89 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇₁×#1473, C₄×#126×C₇₁, C₇₁×#2334, …
maximal normal subgroup of	C₇₁×#1473, C₄×#126×C₇₁, C₇₁×#2334, …
maximal quotient of	C₂×#383×C₇₁, C₂×#387×C₇₁, C₂×#388×C₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 209);

C2×#126×C71 #17985659