C₄₁×#518 #14579986

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×#518

Subgroups

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂⁴
commutator	C₂	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ G

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 656

A minimal faithful permutation representation — 4 generators on 53 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)(46,47)(48,52)(49,50)(51,53);(47,50)(51,52);(46,47)(48,51)(49,50)(52,53);(46,48)(47,51)(49,53)(50,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₁×#1828, C₄₁×#1829, C₄₁×#1856, …
maximal normal subgroup of	C₄₁×#1828, C₄₁×#1829, C₄₁×#1856, …
maximal quotient of	C₄₁×#2273, C₄₁×#2274, C₄₁×#2275, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 199);

C41×#518 #14579986