C₅₉×#10497 #28422606

order	15104
nilpotency class	3
isoclinism	isoclinic class of #10496
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#10497

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
prime radical	C₅₉×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

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

normal subgroups only

This group has 348 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) = 7552

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

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

Conjugacy classes & character table

1829 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 3485);