C₄₁×#446 #14579914

order	2624
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₄₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₄₁×#446

Subgroups

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

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2624

A minimal faithful permutation representation — 3 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)(44,49)(45,47)(46,48)(50,51,53,52,54,55,57,56);(42,44,46,45)(43,47,48,49);(42,45,46,44)(43,47,48,49)(50,52,53,55,54,56,57,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₁×#1338, C₄₁×#1582, C₄₁×#1584, …
maximal normal subgroup of	C₄₁×#1338, C₄₁×#1582, C₄₁×#1584, …
maximal quotient of	C₄₁×#1770, C₄₁×#1771, C₄₁×#1916, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 127);

C41×#446 #14579914