C₁₃₇×#12363 #46861749

order	35072
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃₇×#12363

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃₇	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃₇
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₄²×C₁₃₇ ◁ #446×C₁₃₇ ◁ G

278 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 177
transitive degree	μ_t(G) = 35072

A minimal faithful permutation representation — 3 generators on 177 points:

(2,6)(3,7)(4,8)(9,10,14,18)(11,19,21,38)(12,23,25,37)(13,28,26,17)(15,30,31,20)(16,33,35,27)(22,39,29,34)(24,36,40,32)(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);(1,2,5,3)(4,7,8,6)(9,11,14,21)(10,15,18,31)(12,24,25,40)(13,29,26,22)(16,34,35,39)(17,36,28,32)(19,37,38,23)(20,33,30,27);(1,3,5,2)(4,6,8,7)(12,25)(16,35)(19,38)(20,30)(23,37)(24,40)(27,33)(34,39)

Conjugacy classes & character table

4247 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35072, 5351);