C₅₉×#32758 #28444867

order	15104
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅₉ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₅₉×#32758

Subgroups

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

1092 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 234 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) = 7552

A minimal faithful permutation representation — 4 generators on 83 points:

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

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, 25746);