C₅₉×#8101 #28420210

order	15104
nilpotency class	3
isoclinism	isoclinic class of #8101
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₅₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₅₉×#8101

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#95
commutator	C₂³	C₂×C₄²×C₅₉
Frattini, cosocle	C₂⁵	C₂³×C₅₉
prime radical	C₂⁶×C₅₉	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂⁶×C₅₉ ◁ G

2414 conjugacy classes of subgroups; only the 278 normal subgroups are shown.

normal subgroups only

This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 278 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)(3,9,11,14)(4,7)(5,8)(6,10,13,16)(12,15)(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)(2,6,8,14)(4,11)(5,10)(7,13,15,9)(12,16);(2,7)(6,13)(8,15)(9,14)

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, 1089);