C₁₅₁×#12117 #50317042

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

Aliases

direct product

C₁₅₁×#12117

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₅₁	#1595
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₅₁
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₅₁ ◁ C₂×C₄×C₁₅₁ ◁ C₂×M₁₆×C₁₅₁ ◁ G

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

normal subgroups only

This group has 424 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:

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

Conjugacy classes & character table

3775 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38656, 5105);