C₁₅₁×#13416 #50318341

order	38656
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₅₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₅₁×#13416

Subgroups

	subgroup	G/H
center	C₄×C₁₅₁	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₅₁
socle	C₂×C₁₅₁	#2041
prime radical	#3150×C₁₅₁	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₅₁ ◁ C₂²×C₄×C₁₅₁ ◁ C₂×#97×C₁₅₁ ◁ G

442 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 183
transitive degree	μ_t(G) = 4832

A minimal faithful permutation representation — 3 generators on 183 points:

(1,2)(3,6)(4,17)(5,24)(7,16)(8,13)(9,15)(10,20)(11,26)(12,25)(14,23)(18,27)(19,32)(21,30)(22,31)(28,29)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183);(1,3)(2,9)(4,18)(5,12)(6,24)(7,11)(8,16)(10,22)(13,25)(14,21)(15,26)(17,20)(19,30)(23,29)(27,32)(28,31);(1,4,5,19,8,23,26,22)(2,10,11,29,13,30,24,18)(3,14,15,32,16,17,12,31)(6,27,25,21,7,28,9,20)

Conjugacy classes & character table

5134 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38656, 6404);