C₅₉×#418 #16836952

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

Aliases

direct product

C₅₉×#418

Subgroups

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

190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₉×#1795, C₅₉×#1883, C₅₉×#1887, …
maximal normal subgroup of	C₅₉×#1795, C₅₉×#1883, C₅₉×#1887, …
maximal quotient of	C₅₉×#1478, C₅₉×#1484, C₅₉×#1490, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 99);

C59×#418 #16836952