C₅₉×#7292 #28419401

order	15104
nilpotency class	4
isoclinism	isoclinic class of #7262
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#7292

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#340
commutator	C₂×C₈	C₄²×C₅₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₅₉
prime radical	C₂³×C₅₉	#106
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ C₂×C₄×C₈×C₅₉ ◁ G

198 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 91
transitive degree	μ_t(G) = 7552

A minimal faithful permutation representation — 2 generators on 91 points:

(1,2,4,7,5,8,12,15)(3,9,11,16,10,6,13,14)(18,23,24,25)(19,27)(20,29)(21,28)(26,32,30,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3)(2,6,8,9)(4,11)(5,10)(7,14,15,16)(12,13)(17,18,20,25,21,26,29,32,22,24,19,23,28,30,27,31)

Conjugacy classes & character table

2714 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 280);