C₅₉×#430 #16836964

order	3776
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#430

Subgroups

	subgroup	G/H
center	C₄×C₅₉	C₂×D₄
commutator	C₄	C₂²×C₄×C₅₉
Frattini, cosocle	C₂×C₄	C₂³×C₅₉
socle	C₂×C₅₉	C₂×C₄⋊C₄
prime radical	C₂³×C₅₉	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ G

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 944

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)(60,61,64,67,65,68,63,73)(62,69,72,74,70,75,71,66);(60,62,63,71,65,70,64,72)(61,66,67,69,68,74,73,75);(62,70)(66,74)(69,75)(71,72)

Conjugacy classes & character table

1298 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅₉×#1858, C₅₉×#1861, C₅₉×#1932, …
maximal normal subgroup of	C₅₉×#1858, C₅₉×#1861, C₅₉×#1932, …
maximal quotient of	C₅₉×#1565, C₅₉×#1569, C₅₉×#1570, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 111);

C59×#430 #16836964