C₅₉×#13458 #28425567

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13371
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#13458

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#476
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
prime radical	C₂³×C₅₉	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄×C₈×C₅₉ ◁ G

324 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 3776

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

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

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, 6446);