C₅₉×#13530 #28425639

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#13530

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₉	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ C₂×C₄×C₈×C₅₉ ◁ G

358 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 87
transitive degree	μ_t(G) = 15104

A minimal faithful permutation representation — 3 generators on 87 points:

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

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, 6518);