C₅₉×#12367 #28424476

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12366
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#12367

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#1629
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₅₉
prime radical	C₅₉×#3293	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₄×C₈×C₅₉ ◁ G

336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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:

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

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, 5355);