C₄₁×#519 #14579987

order	2624
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₄₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₄₁×#519

Subgroups

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂⁴
commutator	C₂	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²	C₂⁴×C₄₁
prime radical	C₂³×C₄₁	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ G

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1312

A minimal faithful permutation representation — 4 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)(42,43,44,45)(47,51)(49,57)(52,54)(55,61);(46,47,50,51)(48,54,56,52)(49,53,57,58)(55,60,61,59);(46,48,50,56)(47,52,51,54)(49,55,57,61)(53,59,58,60);(46,49)(47,53)(48,55)(50,57)(51,58)(52,59)(54,60)(56,61)

Conjugacy classes & character table

1394 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₁×#1830, C₄₁×#1857, C₄₁×#1886, …
maximal normal subgroup of	C₄₁×#1830, C₄₁×#1857, C₄₁×#1886, …
maximal quotient of	C₄₁×#2274, C₄₁×#2276, C₄₁×#2310, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 200);

C41×#519 #14579987