C₅₉×#7636 #28419745

order	15104
nilpotency class	3
isoclinism	isoclinic class of #7606
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#7636

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₅₉
Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₄³×C₅₉ ◁ G

436 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 146 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) = 15104

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

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

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, 624);