C₅₉×#10015 #28422124

order	15104
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#10015

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅₉	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
socle	C₂²×C₅₉	#392
prime radical	C₅₉×#2397	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

696 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 1888

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

(1,2,5,8)(3,6,4,7)(9,10,13,16)(11,17,19,24)(12,20,22,15)(14,21,23,18)(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);(2,6)(3,4)(7,8)(9,11)(10,14)(12,21)(13,19)(15,24)(16,23)(17,20)(18,22);(2,7)(3,4)(6,8)(14,23)(17,24)

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, 3003);