C₅₉×#13675 #28425784

order	15104
nilpotency class	5
isoclinism	isoclinic class of #13673
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#13675

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#2196
commutator, Frattini, cosocle	#127	C₂³×C₅₉
prime radical	C₅₉×#3292	C₂
LCS	G ▷ #127 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂²×C₅₉ ◁ C₂×C₄×C₅₉ ◁ #127×C₅₉ ◁ G

408 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 75
transitive degree	μ_t(G) = 944

A minimal faithful permutation representation — 3 generators on 75 points:

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

Conjugacy classes & character table

1475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6663);