C₅₉×#442 #16836976

order	3776
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#442

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×D₄
commutator	C₄	C₂²×C₄×C₅₉
Frattini, cosocle	C₂×C₄	C₂³×C₅₉
prime radical	C₂×D₈×C₅₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 3 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)(60,61,63,62)(64,65,67,69)(66,68,71,70);(65,68)(66,71)(69,70);(60,62,63,61)(65,69)(68,70)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₉×AGL(1,ℤ/16), C₂×C₅₉×#442, C₅₉×#2943, …
maximal normal subgroup of	C₅₉×AGL(1,ℤ/16), C₂×C₅₉×#442, C₅₉×#2943, …
maximal quotient of	C₅₉×#1580, C₅₉×#1586, C₅₉×#1594, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 123);

C59×#442 #16836976