C₁₁₃×#7474 #43275494

order	28928
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁₃×#7474

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁₃	#367
commutator	C₁₆	C₄²×C₁₁₃
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₁₃
prime radical	C₂³×C₁₁₃	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₂²×C₄×C₁₁₃ ◁ C₂²×C₈×C₁₁₃ ◁ C₂²×C₁₆×C₁₁₃ ◁ G

174 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 149
transitive degree	μ_t(G) = 7232

A minimal faithful permutation representation — 2 generators on 149 points:

(1,2)(3,4)(6,12,13,28)(7,17)(8,22)(9,25)(10,19)(14,33,32,15)(16,36,29,31)(18,26)(20,24)(21,23)(27,34,35,30)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149);(2,4)(5,6,8,14,9,15,7,12,19,29,17,30,18,27,22,36,11,13,24,32,26,33,21,28,10,16,23,34,25,35,20,31)

Conjugacy classes & character table

5876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28928, 462);