C₁₅₁×#11920 #50316845

order	38656
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₅₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₅₁×#11920

Subgroups

	subgroup	G/H
center	C₄×C₁₅₁	#331
commutator	C₄²	C₂²×C₄×C₁₅₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₅₁
socle	C₂×C₁₅₁	C₂×#331
prime radical	#3147×C₁₅₁	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₅₁ ◁ C₂²×C₄×C₁₅₁ ◁ C₂×C₄×C₈×C₁₅₁ ◁ G

400 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 138 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:

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

Conjugacy classes & character table

6946 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38656, 4908);