C₁₁₃×#8771 #43276791

order	28928
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁₃×#8771

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁₃	#381
commutator	C₂²×C₄	C₂²×C₄×C₁₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁₃
prime radical	C₂²×D₄×C₁₁₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₂×C₄²×C₁₁₃ ◁ G

426 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 137
transitive degree	μ_t(G) = 7232

A minimal faithful permutation representation — 3 generators on 137 points:

(2,5)(3,6)(7,8)(9,10,15,19,13,20,14,18)(11,16,21,17,12,22,23,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137);(1,2,4,5)(3,6,7,8)(9,11,13,12)(10,16,20,22)(14,21,15,23)(17,19,24,18);(1,3)(2,6)(4,7)(5,8)(9,12,13,11)(10,17)(14,23,15,21)(16,19)(18,22)(20,24)

Conjugacy classes & character table

4859 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28928, 1759);