C₅₉×#8531 #28420640

order	15104
nilpotency class	3
isoclinism	isoclinic class of #8528
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₅₉×#8531

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#379
commutator	C₄²	C₂²×C₄×C₅₉
Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
prime radical	C₅₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

728 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 83
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 3 generators on 83 points:

(1,2,4,6,5,3,7,8)(9,10,14,16,13,12,20,21)(11,15,19,23,18,17,22,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(1,3)(2,5)(4,6)(7,8)(9,11,13,18)(10,15,12,17)(14,22,20,19)(16,24,21,23);(4,7)(6,8)(9,12)(10,13)(11,17)(14,16)(15,18)(19,23)(20,21)(22,24)

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1519);