C₅₉×#7354 #28419463

order	15104
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₅₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₅₉×#7354

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#353
commutator	C₄²	C₂×C₈×C₅₉
Frattini, cosocle	#384	C₂²×C₅₉
prime radical	C₂×#127×C₅₉	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂³×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₅₉×#384 ◁ G

268 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 generators on 83 points:

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

Conjugacy classes & character table

2006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 342);