C₅₉×#559 #16837093

order	3776
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₅₉×#559

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₅₉
prime radical	#127×C₅₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ G

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(60,61,64,63)(62,66,67,65)(69,72)(73,74);(61,63)(65,66)(68,69,71,72)(70,74,75,73);(60,62,64,67)(61,65,63,66);(60,63,64,61)(62,66,67,65)(68,70,71,75)(69,73,72,74)

Conjugacy classes & character table

1475 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅₉×#1620, C₅₉×#1630, C₅₉×#1640, …
maximal normal subgroup of	C₅₉×#1620, C₅₉×#1630, C₅₉×#1640, …
maximal quotient of	C₅₉×#2355, C₅₉×#2357, C₅₉×#2366, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 240);

C59×#559 #16837093