C₅₉×#7479 #28419588

order	15104
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#7479

Subgroups

	subgroup	G/H
center	C₄×C₅₉	#357
commutator	C₁₆	C₄²×C₅₉
Frattini, cosocle	C₂²×C₁₆	C₂²×C₅₉
socle	C₂×C₅₉	#1380
prime radical	C₂³×C₅₉	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂²×C₈×C₅₉ ◁ C₂²×C₁₆×C₅₉ ◁ G

162 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 123
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 2 generators on 123 points:

(1,2,5,11,8,15,28,14)(3,16,18,48,21,39,53,49)(4,22,25,45,26,12,29,43)(6,10,27,40,30,42,61,41)(7,31,24,13,32,44,60,46)(9,33,34,23,38,59,37,17)(19,54,52,64,51,47,62,36)(20,55,50,35,56,63,58,57)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(1,3,6,19,7,20,29,33,28,53,61,62,60,58,26,17,8,21,30,51,32,56,25,59,5,18,27,52,24,50,4,23)(2,9,12,35,13,36,41,48,11,34,43,63,44,54,10,39,15,38,22,57,46,64,40,49,14,37,45,55,31,47,42,16)

Conjugacy classes & character table

3068 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 467);