C₁₄₉×#9979 #49188928

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

Aliases

direct product

C₁₄₉×#9979

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₄₉	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
prime radical	C₂⁴×C₁₄₉	#41
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂³×C₄×C₁₄₉ ◁ G

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 197
transitive degree	μ_t(G) = 9536

A minimal faithful permutation representation — 3 generators on 197 points:

(1,2)(3,6)(4,7)(5,8)(9,12)(10,13)(11,15)(14,16)(17,18,23,27)(19,28,32,40)(20,33,37,43)(21,38,22,26)(24,31,41,30)(25,35,44,36)(29,46,47,39)(34,45,48,42)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197);(1,3,5,10)(2,6,8,13)(4,9,11,16)(7,14,15,12)(17,19)(18,24)(20,34)(21,31)(22,30)(23,32)(25,42)(26,40)(27,41)(28,38)(29,35)(33,39)(36,47)(37,48)(43,46)(44,45);(1,4)(2,7)(3,9)(5,11)(6,12)(8,15)(10,16)(13,14)(17,20,23,37)(18,25,27,44)(19,29,32,47)(21,35,22,36)(24,39,41,46)(26,43,38,33)(28,45,40,42)(30,34,31,48)

Conjugacy classes & character table

5066 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38144, 2967);