C₅₉×#7097 #28419206

order	15104
nilpotency class	4
isoclinism	isoclinic class of #7092
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#7097

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₅₉	#331
commutator	C₄×C₈	C₂×C₄×C₅₉
Frattini, cosocle	C₈²	C₂²×C₅₉
LCS	G ▷ C₄×C₈ ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ C₈²×C₅₉ ◁ G

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

normal subgroups only

This group has 142 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) = 91
transitive degree	μ_t(G) = 15104

A minimal faithful permutation representation — 2 generators on 91 points:

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

Conjugacy classes & character table

2537 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 85);