C₅₉×#7298 #28419407

order	15104
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#7298

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅₉	#102
commutator	C₂×C₈	C₄²×C₅₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₅₉
socle	C₂²×C₅₉	#340
prime radical	C₂³×C₅₉	#103
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ C₂×C₄×C₈×C₅₉ ◁ G

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

normal subgroups only

This group has 216 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) = 83
transitive degree	μ_t(G) = 7552

A minimal faithful permutation representation — 2 generators on 83 points:

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

Conjugacy classes & character table

3422 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 286);