C₅₉×#451 #16836985

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

Aliases

direct product

C₅₉×#451

Subgroups

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

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 3 generators on 79 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)(62,63)(64,65,68,71)(66,72,74,79)(67,75,77,70)(69,76,78,73);(64,66,68,74)(65,69,71,78)(67,76,77,73)(70,79,75,72);(61,63)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₉×#1602, C₅₉×#1603, C₅₉×#1605, …
maximal normal subgroup of	C₅₉×#1602, C₅₉×#1603, C₅₉×#1605, …
maximal quotient of	C₅₉×#1602, C₅₉×#1605, C₅₉×#1614, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 132);

C59×#451 #16836985