C₁₅₁×#12465 #50317390

order	38656
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₅₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₅₁×#12465

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₅₁	#1677
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₅₁
prime radical	#2213×C₁₅₁	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₅₁ ◁ C₂×C₄×C₁₅₁ ◁ C₄×C₈×C₁₅₁ ◁ G

196 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 70 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:

(2,8)(3,13)(4,9)(5,20)(6,19)(11,31)(12,21)(14,15)(16,18)(17,25)(22,27)(23,24)(26,32)(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);(1,2,9,24,6,11,5,21,7,12,20,31,19,23,4,8)(3,10,25,27,15,28,14,26,17,30,13,32,16,29,18,22);(1,3)(2,10)(4,18)(5,14)(6,15)(7,17)(8,22)(9,25)(11,28)(12,30)(13,20)(16,19)(21,26)(23,29)(24,27)(31,32)

Conjugacy classes & character table

4681 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38656, 5453);