C₁₄₉×#7799 #49186748

order	38144
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₄₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₄₉×#7799

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₄₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₄₉
prime radical	C₂²×D₄×C₁₄₉	D₄
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₄₉ ◁ C₂×C₄²×C₁₄₉ ◁ G

404 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 181
transitive degree	μ_t(G) = 19072

A minimal faithful permutation representation — 3 generators on 181 points:

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

Conjugacy classes & character table

5513 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38144, 787);