C₅₉×#32762 #28444871

order	15104
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅₉ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₅₉×#32762

Subgroups

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂⁴×C₅₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

812 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 234 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 — 4 generators on 91 points:

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

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 25750);