C₅₉×#8492 #28420601

order	15104
nilpotency class	3
isoclinism	isoclinic class of #8491
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₅₉×#8492

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#379
commutator	C₄²	C₂²×C₄×C₅₉
Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
prime radical	C₅₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

692 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 99
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 3 generators on 99 points:

(2,5,6,7)(9,10)(11,19,22,15)(12,23,25,32)(13,18)(14,17)(16,24,30,26)(20,35)(21,34,39,29)(27,31)(28,36)(33,38)(37,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,2)(3,7)(4,6)(5,8)(9,11,14,22)(10,15,17,19)(12,20,25,37)(13,21,27,39)(16,28,30,33)(18,29,31,34)(23,40,32,35)(24,36,26,38);(3,8)(5,7)(9,12)(10,16)(11,20)(13,26)(14,25)(15,28)(17,30)(18,32)(19,33)(21,38)(22,37)(23,31)(24,27)(29,35)(34,40)(36,39)

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, 1480);