C₄₁×#533 #14580001

order	2624
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₄₁×#533

Subgroups

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

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1312

A minimal faithful permutation representation — 4 generators on 57 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)(44,47)(45,46)(48,49)(50,51,53,55)(52,56,57,54);(43,46)(47,49);(50,52,53,57)(51,54,55,56);(42,44,45,48)(43,47,46,49)

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₁×#1481, C₄₁×#1485, C₄₁×#1493, …
maximal normal subgroup of	C₄₁×#1481, C₄₁×#1485, C₄₁×#1493, …
maximal quotient of	C₄₁×#2285, C₄₁×#2295, C₄₁×#2296, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 214);

C41×#533 #14580001