C₅₉×#13573 #28425682

order	15104
nilpotency class	5
isoclinism	isoclinic class of #13569
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#13573

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	C₂×AΣL(1,𝔽₁₆)
commutator	C₂×Q₈	C₂²×C₄×C₅₉
Frattini, cosocle	C₄⋊Q₈	C₂³×C₅₉
prime radical	C₂×2₋¹⁺⁴×C₅₉	C₄
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂³×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄⋊Q₈×C₅₉ ◁ G

470 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 91
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 3 generators on 91 points:

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

Conjugacy classes & character table

1652 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6561);