C₅₉×#7393 #28419502

order	15104
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅₉×#7393

Subgroups

	subgroup	G/H
center	C₂×C₈×C₅₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₁₆×C₅₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₅₉
socle, prime radical	C₂²×C₅₉	C₂²⋊C₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₅₉ ◁ C₄×C₁₆×C₅₉ ◁ G

110 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 62 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) = 15104

A minimal faithful permutation representation — 2 generators on 99 points:

(2,5)(3,7)(6,8)(9,10,12,18,14,19,25,33,15,16,23,28,27,29,36,38,13,17,24,30,26,31,37,39,11,20,21,32,22,34,35,40)(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);(1,2,4,6)(3,8,7,5)(9,11,13,15)(10,16,17,20)(12,23,24,21)(14,22,26,27)(18,32,30,28)(19,29,31,34)(25,36,37,35)(33,40,39,38)

Conjugacy classes & character table

4484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 381);