C₅₉×#12438 #28424547

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12436
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#12438

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#1667
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₅₉
prime radical	C₅₉×#2213	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₄×C₈×C₅₉ ◁ G

224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 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:

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

Conjugacy classes & character table

2183 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5426);