#353×C₇₁ #17985484

order	4544
nilpotency class	4
isoclinism	isoclinic class of #353
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

#353×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₁	#99
commutator	C₂×C₄	C₂×C₄×C₇₁
Frattini, cosocle	C₂×D₄	C₂²×C₇₁
prime radical	#127×C₇₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₁ ◁ C₂²×C₇₁ ◁ C₂×D₄×C₇₁ ◁ G

86 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 568

A minimal faithful permutation representation — 2 generators on 79 points:

(1,2)(3,6,8,5)(4,7)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79);(2,5)(3,8)(6,7)

Conjugacy classes & character table

923 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇₁×#1402, C₇₁×#1408, C₇₁×#1409, …
maximal normal subgroup of	C₇₁×#1402, C₇₁×#1408, C₇₁×#1409, …
maximal quotient of	C₇₁×#1318, C₇₁×#1325, C₇₁×#1343, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 34);

#353×C71 #17985484

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

#353×C₇₁ #17985484