C₅₉×#339 #16836873

order	3776
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#339

Subgroups

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

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 944

A minimal faithful permutation representation — 2 generators on 71 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)(66,68)(67,70)(69,71);(65,68,70,69)

Conjugacy classes & character table

1652 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅₉×#339, C₅₉×#1733, C₄×#104×C₅₉, …
maximal normal subgroup of	C₂×C₅₉×#339, C₅₉×#1733, C₄×#104×C₅₉, …
maximal quotient of	C₅₉×#1276, C₅₉×#1278, C₅₉×#1279, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 20);

C59×#339 #16836873