C₅₉×#474 #16837008

order	3776
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#474

Subgroups

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

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 3 generators on 75 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)(70,72)(71,74)(73,75);(60,62,63,67)(61,64,65,66);(69,72)(70,75)(73,74)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₉×#1639, C₅₉×#1641, C₅₉×#1644, …
maximal normal subgroup of	C₅₉×#1639, C₅₉×#1641, C₅₉×#1644, …
maximal quotient of	C₅₉×#1802, C₅₉×#1862, C₅₉×#1918, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 155);

C59×#474 #16837008