C₅₉×#7065 #28419174

order	15104
nilpotency class	4
isoclinism	isoclinic class of #1343
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#7065

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅₉	#99
commutator	C₂²×C₄	C₂×C₈×C₅₉
Frattini, cosocle	C₂×C₄⋊C₈	C₂²×C₅₉
socle	C₂²×C₅₉	#324
prime radical	C₂³×C₅₉	C₂²⋊C₈
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄⋊C₈×C₅₉ ◁ G

156 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 107
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 2 generators on 107 points:

(1,2)(3,9,11,15)(4,12,13,7)(5,8)(6,10)(14,16)(17,18,20,25,21,26,31,39,22,24,30,36,32,37,43,46)(19,23,28,33,29,35,42,44,27,34,40,38,41,45,48,47)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3)(2,6,8,14)(4,10)(5,11)(7,9,12,15)(13,16)(17,19)(18,23,24,34)(20,28)(21,29)(22,27)(25,38,36,33)(26,35,37,45)(30,40)(31,42)(32,41)(39,47,46,44)(43,48)

Conjugacy classes & character table

2714 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 53);