C₅₉×#479 #16837013

order	3776
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#479

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₅₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 3 generators on 83 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59)(60,61,63,65)(62,66,67,64)(68,69,71,73)(70,76,77,83)(72,80,79,75)(74,81,82,78);(60,62,63,67)(61,64,65,66)(69,73)(74,82)(75,80)(76,83);(68,70,71,77)(69,74,73,82)(72,81,79,78)(75,83,80,76)

Conjugacy classes & character table

1121 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅₉×#479, C₅₉×#3076, C₅₉×#3078, …
maximal normal subgroup of	C₂×C₅₉×#479, C₅₉×#3076, C₅₉×#3078, …
maximal quotient of	C₅₉×#1805, C₅₉×#1863, C₅₉×#1865, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 160);

C59×#479 #16837013