C₅₉×#12509 #28424618

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12503
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₅₉×#12509

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₅₉
prime radical	C₅₉×#1712	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ C₈²×C₅₉ ◁ G

306 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 91
transitive degree	μ_t(G) = 7552

A minimal faithful permutation representation — 3 generators on 91 points:

(1,2)(3,9)(4,12)(5,7)(6,10)(8,13)(11,15)(14,16)(18,25)(19,30)(20,21)(22,23)(26,31)(27,29)(28,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3,4,10,5,11,13,16)(2,6,8,9,7,14,12,15)(17,18,26,32,22,28,20,25,24,30,21,27,23,29,31,19);(2,7)(6,14)(8,12)(9,15)(17,19,31,29,23,27,21,30,24,25,20,28,22,32,26,18)

Conjugacy classes & character table

4130 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5497);