C₅₉×#13434 #28425543

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#13434

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₅₉
prime radical	C₅₉×#535	C₂²
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₂×#41×C₅₉ ◁ G

424 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 86 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:

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

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, 6422);