C₅₉×#423 #16836957

order	3776
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#423

Subgroups

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

126 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)(61,63)(64,65,66,69,67,68,70,71);(60,61,62,63);(65,68)(69,71)

Conjugacy classes & character table

1652 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅₉×#1286, C₅₉×#1292, C₅₉×#1299, …
maximal normal subgroup of	C₅₉×#1286, C₅₉×#1292, C₅₉×#1299, …
maximal quotient of	C₅₉×#1566, C₅₉×#1567, C₅₉×#1568, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 104);

C59×#423 #16836957