C₅₉×#7211 #28419320

order	15104
nilpotency class	3
isoclinism	isoclinic class of #1304
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#7211

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅₉	#95
commutator	C₂³	C₄×C₈×C₅₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₅₉
socle	C₂²×C₅₉	#336
prime radical	C₂³×C₅₉	C₄×C₈
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂×C₄×C₈×C₅₉ ◁ G

200 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 102 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:

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

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, 199);