C₅₉×#8734 #28420843

order	15104
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#8734

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#381
commutator	C₂³	C₂²×C₈×C₅₉
Frattini, cosocle	C₂³×C₄	C₂³×C₅₉
prime radical	C₂⁵×C₅₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂³×C₄×C₅₉ ◁ G

622 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 166 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) = 1888

A minimal faithful permutation representation — 3 generators on 83 points:

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

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, 1722);