C₅₉×#8509 #28420618

order	15104
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₅₉×#8509

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₉	#120
commutator	C₄²	C₂²×C₄×C₅₉
Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

656 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 95
transitive degree	μ_t(G) = 15104

A minimal faithful permutation representation — 3 generators on 95 points:

(1,2)(3,4)(5,6,11,14,9,8,10,13)(7,12,18,20,16,15,17,19)(22,26,28,31)(27,35,36,34)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(5,7,9,16)(6,12,8,15)(10,18,11,17)(13,20,14,19)(21,22)(23,27)(24,31)(25,28)(26,33)(29,34)(30,36)(32,35);(2,4)(5,8,9,6)(7,15,16,12)(10,13,11,14)(17,19,18,20)(21,23,25,30)(22,27,28,36)(24,32,33,29)(26,34,31,35)

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1497);