C₅₉×#7144 #28419253

order	15104
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₅₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₅₉×#7144

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅₉	#95
commutator	C₂×C₄	C₄×C₈×C₅₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₅₉
socle	C₂²×C₅₉	#336
prime radical	C₂³×C₅₉	C₂²⋊C₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂×C₄×C₈×C₅₉ ◁ G

210 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 98 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)(4,7)(5,8)(6,10,13,16)(12,14)(17,18,20,24,21,26,31,38,22,25,32,37,33,39,44,47)(19,27,29,40,30,41,43,48,28,23,34,35,42,36,45,46)(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)(2,6,8,13)(4,10)(5,11)(7,9,14,15)(12,16)(17,19)(18,23,25,27)(20,29)(21,30)(22,28)(24,35,37,40)(26,36,39,41)(31,43)(32,34)(33,42)(38,46,47,48)(44,45)

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, 132);