C₅₉×#13642 #28425751

order	15104
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#13642

Subgroups

	subgroup	G/H
center	C₈×C₅₉	#117
commutator	C₂×C₄	C₂²×C₈×C₅₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₅₉
socle	C₂×C₅₉	#2163
prime radical	C₂³×C₅₉	M₃₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₅₉ ◁ C₅₉×#346 ◁ G

170 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 106 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:

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

Conjugacy classes & character table

3776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6630);