C₁₃₁×#7602 #45693486

order	33536
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃₁×#7602

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₁
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₄³×C₁₃₁ ◁ G

408 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 154 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) = 155
transitive degree	μ_t(G) = 33536

A minimal faithful permutation representation — 3 generators on 155 points:

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

Conjugacy classes & character table

6812 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33536, 590);