C₅₉×#342 #16836876

order	3776
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#342

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂²⋊C₄
commutator	C₂²	C₄²×C₅₉
Frattini, cosocle	C₂⁴	C₂²×C₅₉
prime radical	C₂⁴×C₅₉	C₂²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂⁴×C₅₉ ◁ G

142 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)(64,65)(66,70,71,68)(67,69);(60,61,62,63)(64,66)(65,68)(67,71)(69,70)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₉×#1343, C₅₉×#1344, C₅₉×#1351, …
maximal normal subgroup of	C₅₉×#1343, C₅₉×#1344, C₅₉×#1351, …
maximal quotient of	C₅₉×#1280, C₅₉×#1282, C₅₉×#1284, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 23);

C59×#342 #16836876