C₅₉×#7060 #28419169

order	15104
nilpotency class	4
isoclinism	isoclinic class of #1343
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#7060

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅₉	#99
commutator	C₂²×C₄	C₂×C₈×C₅₉
Frattini, cosocle	C₂×C₄⋊C₈	C₂²×C₅₉
socle	C₂²×C₅₉	#323
prime radical	C₂²×D₄×C₅₉	C₈
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄⋊C₈×C₅₉ ◁ G

240 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 3776

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

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

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, 48);