C₁₅₁×#11953 #50316878

order	38656
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₅₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₅₁×#11953

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₅₁	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₅₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₅₁
prime radical	C₂³×C₁₅₁	#102
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₅₁ ◁ C₂×C₄²×C₁₅₁ ◁ C₂×C₄×C₈×C₁₅₁ ◁ G

296 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 199
transitive degree	μ_t(G) = 19328

A minimal faithful permutation representation — 3 generators on 199 points:

(1,2,5,10,6,9,4,8)(3,11,12,16,13,7,14,15)(17,18,21,27,35,43,36,45,23,25,20,26,22,28,38,47)(19,29,31,42,39,46,34,24,33,41,30,48,32,44,37,40)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199);(1,3)(2,7)(4,12)(5,14)(6,13)(8,15)(9,11)(10,16)(17,19,23,33)(18,24,25,40)(20,34,21,37)(22,39,35,32)(26,44,27,46)(28,48,43,42)(29,47,41,45)(30,38,31,36);(1,4,6,5)(2,8,9,10)(3,12,13,14)(7,15,11,16)(18,25)(24,40)(26,27)(28,43)(29,41)(42,48)(44,46)(45,47)

Conjugacy classes & character table

6946 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38656, 4941);