C₅₉×#12419 #28424528

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12416
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#12419

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₅₉
prime radical	C₅₉×#493	C₂²
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ C₈²×C₅₉ ◁ G

240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 82 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 — 3 generators on 83 points:

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

Conjugacy classes & character table

2537 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5407);