C₄₁×#334 #14579802

order	2624
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₄₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₄₁×#334

Subgroups

	subgroup	G/H
center	C₂×C₄×C₄₁	D₄
commutator	C₄	C₂×C₈×C₄₁
Frattini, cosocle	C₄²	C₂²×C₄₁
socle, prime radical	C₂²×C₄₁	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₄²×C₄₁ ◁ G

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 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)(43,46)(44,48)(47,49)(50,51,52,54,53,55,56,57);(42,43,44,46,45,47,48,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₁×#1333, C₄₁×#1334, C₄₁×#1360, …
maximal normal subgroup of	C₄₁×#1333, C₄₁×#1334, C₄₁×#1360, …
maximal quotient of	C₄₁×#1277, C₄₁×#1367, C₄₁×#1368, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 15);

C41×#334 #14579802